Question

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

Answer 1

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

Since -6 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 6 to both sides.
-4(x+10)=6-3(x-2)

Multiply -3 by each term inside the parentheses (x-2).
-4(x+10)=6+(-3(x)-3(-2))

Multiply -3 by the x inside the parentheses.
-4(x+10)=6+(-3*x-3(-2))

Multiply -3 by x to get -3x.
-4(x+10)=6+(-3x-3(-2))

Multiply -3 by the -2 inside the parentheses.
-4(x+10)=6+(-3x+3*2)

Multiply 3 by 2 to get 6.
-4(x+10)=6+(-3x+6)

Remove the parentheses around the expression -3x+6.
-4(x+10)=6-3x+6

Add 6 to 6 to get 12.
-4(x+10)=12-3x

Reorder the polynomial 12-3x alphabetically from left to right, starting with the highest order term.
-4(x+10)=-3x+12

Multiply -4 by each term inside the parentheses (x+10).
(-4(x)-4(10))=-3x+12

Multiply -4 by the x inside the parentheses.
(-4*x-4(10))=-3x+12

Multiply -4 by x to get -4x.
(-4x-4(10))=-3x+12

Multiply -4 by the 10 inside the parentheses.
(-4x-4*10)=-3x+12

Multiply -4 by 10 to get -40.
(-4x-40)=-3x+12

Remove the parentheses around the expression -4x-40.
-4x-40=-3x+12

Since -3x contains the variable to solve for, move it to the left-hand side of the equation by adding 3x to both sides.
-4x-40+3x=12

According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, x is a factor of both -4x and 3x.
(-4+3)x-40=12

To add integers with different signs, subtract their absolute values and give the result the same sign as the integer with the greater absolute value. In this example, subtract the absolute values of -4 and 3 and give the result the same sign as the integer with the greater absolute value.
(-1)x-40=12

Remove the parentheses.
-x-40=12

Since -40 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 40 to both sides.
-x=40+12

Add 12 to 40 to get 52.
-x=52

Multiply each term in the equation by -1.
-x*-1=52*-1

Multiply -x by -1 to get x.
x=52*-1

Multiply 52 by -1 to get -52.
x=-52