1. Section 7.1
Exercise 33 Page 292
Subchapter links expand_more
Sign In
To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the properties of equality. In this case, we need to start by using the Distributive Property to simplify the left-hand side of the equation.
Distribute -2
Multiply
Now we can continue to solve using the properties of equality.
LHS+8=RHS+8
LHS+1/2x=RHS+1/2x
a=a/1
a/b=a * 4/b * 4
a/c* b = a* b/c
a/b=a * 2/b * 2
Multiply
Add and subtract fractions
Add and subtract terms
Next, we will use the Multiplication and Division Properties of Equality to isolate x.
LHS * 4=RHS* 4
a/4* 4 = a
Multiply
.LHS /(- 11).=.RHS /(- 11).
Calculate quotient
We found that x=- 3 is the solution to the equation.
To check our solution, we will substitute it into the original equation and simplify. If we end up with a true statement, we will know that our answer is correct. Let's do it!
x= - 3
Multiply
Subtract term
Multiply
Calculate quotient
Add and subtract terms
We got a true statement, so our solution is correct!
To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the properties of equality. In this case, we will move the constant terms to the right-hand side of the equation.
Rewrite 1 as 5/5
Add and subtract terms
LHS-7/5=RHS-7/5
Put minus sign in front of fraction
Now let's simplify both sides of the equation.
Calculate quotient
Write as a sum
Write as a sum of fractions
Calculate quotient
Add terms
Finally, we can use the Division Property of Equality to isolate x.
The solution to the equation is x=0.7.
We can check our solution by substituting it into the original equation.
x= 0.7
a/c* b = a* b/c
Multiply
Subtract fractions
LHS * 15=RHS* 15
a*b/c= a* b/c
Multiply
Calculate quotient
Add and subtract terms
Since the left-hand side is equal to the right-hand side, our solution is correct.