Solving One-Step Equations with Rational Coefficients

We have been given a sentence and we want to translate it into an equation.

Seven times k is equal to twelve.

Every equation has an equals sign and values or expressions on either side of it. Key phrases, such as is, is equal to, and equals tell us about the placement of the equals sign. Let's look for such a keyword in the given sentence and replace it with the equals sign. Seven timesk is equal to twelve. ⇕ Seven timesk = twelve. On the left-hand side we have another keyword times. This word tells us the operation that will be used in our equation, which is multiplication. Seven times k 7 * k On the right-hand side, we have the number twelve. Putting these sides together, we have a complete equation. 7 * k = 12

We want to translate the given sentence into an equation.

Forty-one is one and a half times x.

Like every equation, our equation will have an equals sign and values or expressions on either side of it. Key phrases, like is, is equal to, and equals tell us where the equals sign should be placed. Forty-one is one and a half timesx. ⇕ Forty-one = one and a half timesx. The left-hand side is the number forty-one. On the right-hand side, we have the keyword times. This means that we will use multiplication in our equation. one and a half times x 1.5 * x Putting the two sides together, we have a complete equation. 41 = 1.5 * x

Let's translate the given sentence into an equation.

The product of n and 5 equals 22.

Like all equations, ours will have an equals sign and values or expressions on either side of it. Key phrases, for example is, is equal to, and equals tell us where to put the equals sign. The product ofnand5 equals 22. ⇕ The product ofnand5 = 22. On the left-hand side we have the keyword product. This word tells us that multiplication will be used in our equation. The product of n and 5 n * 5 On the right-hand side, we have the number 22. Putting these sides together, we have a complete equation. n * 5 = 22

We are given the following sentence and we want to translate it into an equation.

The number k divided by eight is equal to four.

Every equation has an equals sign and values or expressions on either side of it. Key phrases, such as is, is equal to, and equals helps us determine where to put the equal sign. The numberk divided by eight is equal to four. ⇕ The numberk divided by eight = four. On the left-hand side we have the key phrase divided by. This tells us the operation that will be used in our equation, which is division. The numberk divided by eight k ÷ 8 On the right-hand side, we have the number four. Putting these sides together, we have a complete equation. k ÷ 8 = 4

We want to translate the given sentence into an equation.

Fourteen is v divided by five.

Like every equation, our equation will have an equals sign and values or expressions on either side of it. Key phrases, like is, is equal to, and equals tell us where the equals sign should be placed. Fourteen is vdivided by five. ⇕ Fourteen = vdivided by five. The left-hand side is the number fourteen. On the right-hand side, we have the key phrase divided by. This means that we will use division in our equation. v divided by five v ÷ 5 Putting the two sides together, we have a complete equation. 14 = v ÷ 5

Let's translate the given sentence into an equation.

The quotient of p and 2 equals 13.

Like all equations, ours will have an equals sign and values or expressions on either side of it. Key phrases, for example is, is equal to, and equals tell us where to put the equals sign. The quotient ofpand2 equals 13. ⇕ The quotient ofpand2 = 13. On the left-hand side we have the keyword quotient. This tells us that division will be used in our equation. The quotient of p and 2 p ÷ 2 On the right-hand side, we have the number 13. Putting these sides together, we have a complete equation. p ÷ 2 = 13

We have to isolate the variable x on one side to solve the given equation. 4x = 24 In this equation, x is multiplied by 4. To undo this multiplication, we need to divide both sides by 4 because multiplication and division are inverse operations. We can perform this division because of the Division Property of Equality. Let's do it!

Our calculations show that the solution to the given equation is x=6. To check that this solution is correct, let's substitute x=6 into the original equation and simplify.

The left-hand side and right-hand side are equal, so x=6 is the correct solution.

For this equation, we need to isolate u on one side. -2 u = 8 Here, the variable u is multiplied by - 2. Dividing by - 2 is the inverse of multiplying by - 2. Let's use the Division Property of Equality to divide both sides of the equation by - 2. This will isolate u.

The solution to the given equation is u=- 4. Finally, we substitute u=- 4 into the original equation and check if our answer is correct.

Substituting u=- 4 resulted in a true statement. We can conclude that u=- 4 is the correct solution.

This time, we will isolate the variable r to solve the equation. 7r = - 3 We can see that r is multiplied by 7. We will use the Division Property of Equality to divide both sides of the equation by 7. This will undo multiplying by 7 and isolate r.

The solution to the given equation is r=- 37. Now, let's verify that our answer is correct. We will substitute r=- 37 into the original equation and simplify to check that our answer is correct.

This statement is true, so r=- 37 is the correct solution.

We have to isolate the variable a on one side to solve the given equation. a ÷ 4 = 9 In this equation, the variable a is divided by 4. Since the inverse of dividing by 4 is multiplying by 4, we will multiply both sides of the equation by 4. The operations will undo each other and the variable is isolated. Let's use the Multiplication Property of Equality to do what we just said.

Our calculations show that the solution to the given equation is a=36. To check that this solution is correct, we will substitute 36 for x into the original equation and simplify.

The left-hand side and right-hand side are equal. This means that a=36 is the correct solution.

Let's solve this equation. 5 = p/4 We need to isolate the variable p on one side to find its solution. We see that p is divided by 4. In this case, we can eliminate the denominator of the fraction by multiplying both sides of the equation by 4. Recall that we are allowed to do so by the Multiplication Property of Equality.

The solution to the given equation is p=20. We can substitute 20 for p into the original equation and simplify to check that our answer is correct.

This statement is true, so p=20 is the correct solution.

We will solve the given equation. We need to isolate the variable h on one side. h/- 4 = 7 In this equation, h is divided by - 4. Again, we will use the Multiplication Property of Equality. If we multiply both sides of the equation by - 4, the variable h will be isolated. This is because multiplying by - 4 is the inverse of dividing by - 4.

The solution to the given equation is h=- 28. Now, let's verify that our answer is correct. We will substitute h=- 28 into the original equation and simplify to check that our answer is correct.

This statement is true, so h=- 28 is the correct solution.

Let's take a look at the given equation. 2/3q = 16 We will isolate the variable q on one side to solve this equation. We see that q is multiplied by a fraction, 23. In other words, the coefficient of the variable is 23. In this case, we can isolate q by multiplying both sides of the equation by the reciprocal of the coefficient. Recall that the reciprocal of a fraction is found by interchanging the numerator and denominator. Fraction & Reciprocal 2/3 & 3/2 Let's multiply both sides by 32. We are allowed to do it by the Multiplication Property of Equality.

Our calculations show that the solution to the given equation is q=24. To check that this solution is correct, let's substitute 24 for q into the original equation and simplify.

The left-hand side and right-hand side are equal, so q=24 is the correct solution.

Let's now solve this equation. - 5/8k = 10 We will isolate k on one side. Here, the variable k is multiplied by - 58. This is a fraction, so we will multiply both sides of the equation by its reciprocal. Fraction & Reciprocal - 5/8 & - 8/5 Let's multiply the equation by the reciprocal.

The solution to the given equation is k=- 16. We can substitute - 16 for k into the original equation and simplify to check that our answer is correct.

This statement is true, so k=- 16 is the correct solution.

Finally, we will solve the following equation. 4/7g = - 12 We need to isolate the variable. We can do it by multiplying both sides of the equation by the reciprocal of the coefficient. The reciprocal of the coefficient 47 is 74. Fraction & Reciprocal 4/7 & 7/4 Let's solve the equation!

The solution to this equation is g=- 21. Now, let's verify that our answer is correct. We will substitute -21 for g in the original equation and simplify to check that our answer is correct.

This statement is true, so g=-21 is the correct solution.