In this section, you will learn how to solve for an algebraic expression, when the value of another expression or the value of a variable is given.
Example 1 :
If 7(a + b) = 2, what is the value of (a + b)?
Solution :
7(a + b) = 2
Divde both sides by 7.
a + b = ²⁄₇
Example 2 :
If 3x + 2 = 7, find the value of 6x - 5.
Solution :
3x + 2 = 7
Subtract 2 from both sides.
3x = 5
Multiply both sides by 2.
6x = 10
Subtract 5 from both sides.
6x - 5 = 5
Example 3 :
If 5x + 5 = 3x - 3, what is the value of 4x - 9?
Solution :
5x + 5 = 3x - 3
Subtract 3x from both sides.
2x + 5 = -3
Subtract 5 from both sides.
2x = -8
Multiply both sides by 2.
4x = -16
Subtract 9 from both sides.
4x - 9 = -25
Example 4 :
Which of the following is equivalent to 2(x + 3) - 7?
(A) 2x - 2
(B) 2x - 1
(C) 2x + 1
(D) 2x + 2
Solution :
= 2(x + 3) - 7
Distribute the 2 to both terms in the parenthses, then combine the numerical constants.
= 2(x) + 2(3) - 7
= 2x + 6 - 7
= 2x - 1
The correct Answer choice is (B).
Example 5 :
Find the value of the following expression
3(5 - 3x) + 7,
if x = -2.
Solution :
= 3(5 - 3x) + 7
Substitute x = -2.
= 3[5 - 3(-2)] + 7
= 3[5 + 6] + 7
= 3(11) + 7
= 33 + 7
= 40
Example 6 :
Find the value of the following expression
a^{2} - b^{2},
if a = 3 and b = -5.
Solution :
= a^{2} - b^{2}
Substitute a = 3 and b = -5.
= a^{2} - b^{2}
= 3^{2} - (-5)^{2}
= 9 - 25
= -16
Example 7 :
If 3x + 8 = 2(y + 4), find the value of ˣ⁄y.
Solution :
3x + 8 = 2(y + 4)
Distribute the 2 to both terms in the parenthses.
3x + 8 = 2(y) + 2(4)
3x + 8 = 2y + 8
Subtract 8 from both sides.
3x = 2y
Divide both sides by y.
³ˣ⁄y = 2
Multiply both sides by ⅓.
(³ˣ⁄y)(⅓) = 2(⅓)
ˣ⁄y = ⅔
Example 8 :
If ²ᵐ⁄n = ⅗, what is the value of ⁿ⁄m?
Solution :
²ᵐ⁄n = ⅗
Multiply both sides by ½.
(½)(²ᵐ⁄n) = (½)(⅗)
ᵐ⁄n = ³⁄₁₀
Take reciprocal on both sides.
ⁿ⁄m = ¹⁰⁄₃
Example 9 :
When 6 times the number n is added to 8, the result is 2. What number results when 3 times n is added to 4?
Solution :
From the given information,
6n + 8 = 2
Subtract 8 from both sides.
6n = -6
Divide both sides by 2.
3n = -3
Add 4 to both sides.
3n + 4 = 1
Adding 4 to 3 times n results 1.
Example 10 :
Subtracting 15 from 14 times of the number k results 13. If 5 is subtracted from 7 times k, what is the result?
Solution :
From the given information,
14k - 15 = 13
Add 15 to both sides.
14k = 28
Divide both sides by 2.
7k = 14
Subtract 5 from both sides.
7k - 5 = 9
Subtracting 5 from 7 times k results 9.
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