Question

Solve the equation: −4(x + 10) − 6 = −3(x − 2

Answer 1

Solve for x:
-6-4 (x+10) = -3 (x-20)
Distribute -4 over x+10.
-4 (x+10) = -40-4 x:
-40-4 x-6 = -3 (x-20)
Group like terms in -4 x-40-6.
Grouping like terms, -4 x-40-6 = -4 x+(-6-40):
-4 x+(-6-40) = -3 (x-20)
Evaluate -6-40.
-6-40 = -46:
-46-4 x = -3 (x-20)
Factor the polynomial, -4 x-46.
Factor -2 from the polynomial -46-4 x:
-2 (2 x+23) = -3 (x-20)
Move everything to the left hand side.
Add 3 (x-20) to both sides of -2 (2 x+23) = -3 (x-20):
3 (x-20)-2 (2 x+23) = 3 (x-20)-3 (x-20)
Look for two terms that sum to zero.
3 (x-20)-3 (x-20) = 0:
3 (x-20)-2 (2 x+23) = 0
Distribute -2 over 2 x+23.
-2 (2 x+23) = -46-4 x:
-46-4 x+3 (x-20) = 0
Distribute 3 over x-20.
3 (x-20) = 3 x-60:
3 x-60-4 x-46 = 0
Group like terms in 3 x-4 x-60-46.
Grouping like terms, 3 x-4 x-60-46 = (3 x-4 x)+(-46-60):
(3 x-4 x)+(-46-60) = 0
Combine like terms in 3 x-4 x.
3 x-4 x = -x:
-x+(-46-60) = 0
Evaluate -46-60.
-46-60 = -106:
-106-x = 0
Isolate terms with x to the left hand side.
Add 106 to both sides:
(106-106)-x = 106
Look for two terms that sum to zero.
106-106 = 0:
-x = 106
Solve for x.
Multiply both sides of -x = 106 by -1:
-x/(-1) = -106
Any nonzero number divided by itself is one.
(-1)/(-1) = 1:
Answer: |
| x = -106

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Answer 2

Simplifying
-4(x + 10) + -6 = -3(x + -2)

Reorder the terms:
-4(10 + x) + -6 = -3(x + -2)
(10 * -4 + x * -4) + -6 = -3(x + -2)
(-40 + -4x) + -6 = -3(x + -2)

Reorder the terms:
-40 + -6 + -4x = -3(x + -2)

Combine like terms: -40 + -6 = -46
-46 + -4x = -3(x + -2)

Reorder the terms:
-46 + -4x = -3(-2 + x)
-46 + -4x = (-2 * -3 + x * -3)
-46 + -4x = (6 + -3x)

Solving
-46 + -4x = 6 + -3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3x' to each side of the equation.
-46 + -4x + 3x = 6 + -3x + 3x

Combine like terms: -4x + 3x = -1x
-46 + -1x = 6 + -3x + 3x

Combine like terms: -3x + 3x = 0
-46 + -1x = 6 + 0
-46 + -1x = 6

Add '46' to each side of the equation.
-46 + 46 + -1x = 6 + 46

Combine like terms: -46 + 46 = 0
0 + -1x = 6 + 46
-1x = 6 + 46

Combine like terms: 6 + 46 = 52
-1x = 52

Divide each side by '-1'.
x = -52

Simplifying
x = -52