Solve : 2 (x - 5) + 3 (x - 2) = 8 + 7 (x - 4) and check your answer.
Answers
Step-by-step explanation:
Simplifying
2(x + -5) + 3(x + -2) = 8 + 7(x + -4)
Reorder the terms:
2(-5 + x) + 3(x + -2) = 8 + 7(x + -4)
(-5 * 2 + x * 2) + 3(x + -2) = 8 + 7(x + -4)
(-10 + 2x) + 3(x + -2) = 8 + 7(x + -4)
Reorder the terms:
-10 + 2x + 3(-2 + x) = 8 + 7(x + -4)
-10 + 2x + (-2 * 3 + x * 3) = 8 + 7(x + -4)
-10 + 2x + (-6 + 3x) = 8 + 7(x + -4)
Reorder the terms:
-10 + -6 + 2x + 3x = 8 + 7(x + -4)
Combine like terms: -10 + -6 = -16
-16 + 2x + 3x = 8 + 7(x + -4)
Combine like terms: 2x + 3x = 5x
-16 + 5x = 8 + 7(x + -4)
Reorder the terms:
-16 + 5x = 8 + 7(-4 + x)
-16 + 5x = 8 + (-4 * 7 + x * 7)
-16 + 5x = 8 + (-28 + 7x)
Combine like terms: 8 + -28 = -20
-16 + 5x = -20 + 7x
Solving
-16 + 5x = -20 + 7x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-7x' to each side of the equation.
-16 + 5x + -7x = -20 + 7x + -7x
Combine like terms: 5x + -7x = -2x
-16 + -2x = -20 + 7x + -7x
Combine like terms: 7x + -7x = 0
-16 + -2x = -20 + 0
-16 + -2x = -20
Add '16' to each side of the equation.
-16 + 16 + -2x = -20 + 16
Combine like terms: -16 + 16 = 0
0 + -2x = -20 + 16
-2x = -20 + 16
Combine like terms: -20 + 16 = -4
-2x = -4
Divide each side by '-2'.
x = 2
Simplifying
x = 2
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Answer:
2
Step-by-step explanation:
2 (x - 5) + 3 (x - 2) = 8 + 7 (x - 4)
2x - 10 + 3x - 6 = 8 + 7x - 28
5x - 16 = 7x - 20
7x - 5x = -16 + 20
2x = 4
x = 2
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