Core Connections: Course 3
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Core Connections: Course 3 View details
2. Section 8.2
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Exercise 92 Page 368

Practice makes perfect
To solve an equation, we 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.
x-3/5=1 25
x=1 25+3/5
Next, we will simplify the right-hand side of the equation using mental math. Notice that 25 and 35 add up to 1.
x=1 25+3/5
x=1+2/5+3/5
x=1+1
x=2

Checking Our Answer

Checking Our Answer
We can check our answer by substituting 2 for x and simplifying. If we get a true statement, our answer is correct. Let's do it!
x-3/5=1 25
2-3/5? =1 25
â–Ľ
Simplify
10/5-3/5? =1 25
10-3/5? =1 25
7/5? =1 25
7/5? =1* 5 + 2/5
7/5? =5 + 2/5
7/5=7/5 âś“
Our solution is correct because the left-hand side is equal to the right-hand side.
We are asked to solve the given equation for x. Let's first gather all of the variable terms on one side of the equation and all of the constant terms on the other.
5.2+x=10.95
x=5.75

Checking Our Answer

Checking Our Answer
Let's check our answer by substituting 5.75 for x and simplifying. If we get a true statement, our answer is correct.
5.2+x=10.95
5.2+ 5.75 ? =10.95
10.95=10.95 âś“
Since the left-hand side is equal to the right-hand side, our solution is correct.
We want to solve the given equation. Let's do it!
2x-3.25=7.15
2x=10.4
x=10.4/2
x=5.2

Checking Our Answer

Checking Our Answer
We can check our answer by substituting 5.2 for x and simplifying. If we get a true statement, our answer is correct. Let's do it!
2x-3.25=7.15
2( 5.2)-3.25? =7.15
â–Ľ
Simplify
10.4-3.25? =7.15
7.15=7.15 âś“
Our solution is correct because the left-hand side is equal to the right-hand side.
Let's consider the given equation. x/16=3/8 Notice that we can expand the fraction on the right-hand side to one with a denominator of 16. Then, the value of x will be the numerator of the fraction on the right-hand side of the equation. Let's do it! 1{\dfrac{x}{16}=\dfrac{3\times 2}{8\times 2} \\[0.7em] \downarrow \\[0.4em] \dfrac{{\color{#0000FF}{x}}}{{\color{#FF0000}{16}}}=\dfrac{{\color{#0000FF}{6}}}{{\color{#FF0000}{16}}}} We can see that x= 6.

Checking Our Answer

Checking Our Answer
Let's check our answer by substituting 6 for x and simplifying. If we get a true statement, our answer is correct.
x/16=3/8
6/16 ? =3/8
â–Ľ
Simplify
6Ă· 2/16Ă· 2 ? =3/8
3/8=3/8 âś“
Since the left-hand side is equal to the right-hand side, our solution is correct.