Question

2x + 4(x - 1) = -10
4(x + 3) - 2 = 6

Explanation:

Solving \( 2x + 4(x - 1) = -10 \)

Step1: Distribute the 4

Use the distributive property \( a(b - c)=ab - ac \) to expand \( 4(x - 1) \).
\( 2x+4x - 4=-10 \)

Step2: Combine like terms

Combine the \( x \)-terms \( 2x \) and \( 4x \).
\( 6x - 4=-10 \)

Step3: Add 4 to both sides

Add 4 to each side to isolate the term with \( x \).
\( 6x-4 + 4=-10 + 4 \)
\( 6x=-6 \)

Step4: Divide by 6

Divide both sides by 6 to solve for \( x \).
\( \frac{6x}{6}=\frac{-6}{6} \)
\( x = - 1 \)

Solving \( 4(x + 3)-2 = 6 \)

Step1: Add 2 to both sides

Add 2 to each side to isolate the term with the parenthesis.
\( 4(x + 3)-2 + 2=6 + 2 \)
\( 4(x + 3)=8 \)

Step2: Divide by 4

Divide both sides by 4 to simplify the equation.
\( \frac{4(x + 3)}{4}=\frac{8}{4} \)
\( x + 3=2 \)

Step3: Subtract 3 from both sides

Subtract 3 from each side to solve for \( x \).
\( x+3 - 3=2 - 3 \)
\( x=-1 \)

Answer:

For \( 2x + 4(x - 1)=-10 \), \( x=-1 \); for \( 4(x + 3)-2 = 6 \), \( x=-1 \)