Question

#10. solve the equation below.
$-4 = 3 + 7(x - 1)$

Explanation:

Solving \( 3(3x + 4) - 5 = -2 \)

Step 1: Expand the bracket

First, we expand the left - hand side of the equation \( 3(3x + 4)-5=-2 \). Using the distributive property \( a(b + c)=ab+ac \), where \( a = 3 \), \( b=3x \) and \( c = 4 \), we get:
\( 3\times3x+3\times4-5=-2 \)
\( 9x + 12-5=-2 \)

Step 2: Simplify the left - hand side

Simplify \( 9x+12 - 5 \). Combine the constant terms \( 12-5 = 7 \), so the equation becomes:
\( 9x+7=-2 \)

Step 3: Isolate the term with \( x \)

Subtract 7 from both sides of the equation to isolate the term with \( x \). According to the subtraction property of equality (if \( a=b \), then \( a - c=b - c \)), we have:
\( 9x+7 - 7=-2 - 7 \)
\( 9x=-9 \)

Step 4: Solve for \( x \)

Divide both sides of the equation by 9. Using the division property of equality (if \( a=b \), then \( \frac{a}{c}=\frac{b}{c} \) for \( c
eq0 \)):
\( \frac{9x}{9}=\frac{-9}{9} \)
\( x=- 1 \)

Step 1: Expand the bracket

First, expand the right - hand side of the equation \( -4 = 3+7(x - 1) \). Using the distributive property \( a(b - c)=ab-ac \), where \( a = 7 \), \( b=x \) and \( c = 1 \), we get:
\( -4=3+7x-7 \)

Step 2: Simplify the right - hand side

Simplify \( 3 + 7x-7 \). Combine the constant terms \( 3-7=-4 \), so the equation becomes:
\( -4=7x-4 \)

Step 3: Isolate the term with \( x \)

Add 4 to both sides of the equation. According to the addition property of equality (if \( a=b \), then \( a + c=b + c \)):
\( -4 + 4=7x-4 + 4 \)
\( 0=7x \)

Step 4: Solve for \( x \)

Divide both sides of the equation by 7:
\( \frac{0}{7}=\frac{7x}{7} \)
\( x = 0 \)

Step 1: Expand the bracket

First, expand the left - hand side of the equation \( -5(2x + 6)+3x=-32 \). Using the distributive property \( a(b + c)=ab+ac \), where \( a=-5 \), \( b = 2x \) and \( c = 6 \), we get:
\( -5\times2x-5\times6+3x=-32 \)
\( -10x-30 + 3x=-32 \)

Step 2: Simplify the left - hand side

Combine like terms \( -10x+3x=-7x \), so the equation becomes:
\( -7x-30=-32 \)

Step 3: Isolate the term with \( x \)

Add 30 to both sides of the equation. Using the addition property of equality:
\( -7x-30 + 30=-32 + 30 \)
\( -7x=-2 \)

Step 4: Solve for \( x \)

Divide both sides of the equation by - 7. Using the division property of equality:
\( \frac{-7x}{-7}=\frac{-2}{-7} \)
\( x=\frac{2}{7} \)

Answer:

\( x=-1 \)

Solving \( - 4=3 + 7(x - 1) \)