Sure, let's fill in the steps and justifications used to solve the given equation step-by-step:
1. Given
[tex]\[ 4x - 7 + 2x = -2x + 12 + 2x \][/tex]
2. Simplification
[tex]\[ 4x - 7 + 2x = -2x + 12 + 2x \][/tex]
Combine like terms:
[tex]\[ 6x - 7 = 12 \][/tex]
3. Addition property of equality
[tex]\[ 6x - 7 + 7 = 12 + 7 \][/tex]
Simplifies to:
[tex]\[ 6x = 19 \][/tex]
4. Division property of equality
Divide both sides by 6:
[tex]\[ x = \frac{19}{6} \][/tex]
5. Simplification
The final value of [tex]\( x \)[/tex]:
[tex]\[ x = \frac{19}{6} \][/tex]
So, the completed solution looks like this:
1. Given
[tex]\[ 4x - 7 + 2x = -2x + 12 + 2x \][/tex]
2. Simplification
[tex]\[ 6x - 7 = 12 \][/tex]
3. Addition property of equality
[tex]\[ 6x - 7 + 7 = 12 + 7 \][/tex]
[tex]\[ 6x = 19 \][/tex]
4. Division property of equality
[tex]\[ x = \frac{19}{6} \][/tex]
5. Simplification
[tex]\[ x = \frac{19}{6} \][/tex]
