Question

th sides of the equation. if both sides are

1. $6x + 1 - 4x = x + 7$; $x = 8$
2. $7x - 5 = 2(3x + 1)$; $x = -3$

Explanation:

Problem 2: \( 6x + 1 - 4x = x + 7 \); \( x = 8 \)

Step 1: Simplify the left - hand side

Combine like terms on the left side of the equation. The like terms with \( x \) are \( 6x \) and \( - 4x \). So \( 6x-4x + 1=(6 - 4)x+1 = 2x + 1 \). The equation becomes \( 2x+1=x + 7 \).

Step 2: Substitute \( x = 8 \) into the left - hand side

Substitute \( x = 8 \) into \( 2x + 1 \). We get \( 2\times8+1=16 + 1=17 \).

Step 3: Substitute \( x = 8 \) into the right - hand side

Substitute \( x = 8 \) into \( x + 7 \). We get \( 8+7 = 15 \).
Since \( 17
eq15 \), \( x = 8 \) is not a solution of the equation \( 6x + 1-4x=x + 7 \).

Problem 4: \( 7x-5 = 2(3x + 1) \); \( x=-3 \)

Step 1: Simplify the right - hand side

First, expand the right - hand side using the distributive property \( a(b + c)=ab+ac \). For \( 2(3x + 1) \), we have \( 2\times3x+2\times1 = 6x+2 \). The equation becomes \( 7x-5=6x + 2 \).

Step 2: Substitute \( x=-3 \) into the left - hand side

Substitute \( x=-3 \) into \( 7x-5 \). We get \( 7\times(-3)-5=-21 - 5=-26 \).

Step 3: Substitute \( x=-3 \) into the right - hand side

Substitute \( x=-3 \) into \( 6x + 2 \). We get \( 6\times(-3)+2=-18 + 2=-16 \).
Since \( - 26
eq-16 \), \( x=-3 \) is not a solution of the equation \( 7x - 5=2(3x + 1) \).

Answer:

• For the equation \( 6x + 1-4x=x + 7 \), \( x = 8 \) is not a solution.
• For the equation \( 7x - 5=2(3x + 1) \), \( x=-3 \) is not a solution.