To determine if the models given by Val and Tia are correct, let's analyze both equations step by step:
### Val's Equation: [tex]\(-2x + 7 = 3x + (-4)\)[/tex]
1. Combine like terms involving [tex]\(x\)[/tex]:
Move the [tex]\(3x\)[/tex] term to the left side by subtracting [tex]\(3x\)[/tex] from both sides.
[tex]\[
-2x - 3x + 7 = -4
\][/tex]
2. Simplify the equation:
Combine the [tex]\(x\)[/tex]-terms.
[tex]\[
-5x + 7 = -4
\][/tex]
3. Isolate [tex]\(x\)[/tex]:
Subtract 7 from both sides.
[tex]\[
-5x = -4 - 7
\][/tex]
Simplify the right side.
[tex]\[
-5x = -11
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by -5.
[tex]\[
x = \frac{11}{5}
\][/tex]
### Tia's Equation: [tex]\(7 - 2x = (-4) + 3x\)[/tex]
1. Combine like terms involving [tex]\(x\)[/tex]:
Move the [tex]\(3x\)[/tex] term to the left side by subtracting [tex]\(3x\)[/tex] from both sides.
[tex]\[
7 - 2x - 3x = -4
\][/tex]
2. Simplify the equation:
Combine the [tex]\(x\)[/tex]-terms.
[tex]\[
7 - 5x = -4
\][/tex]
3. Isolate [tex]\(x\)[/tex]:
Subtract 7 from both sides.
[tex]\[
-5x = -4 - 7
\][/tex]
Simplify the right side.
[tex]\[
-5x = -11
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by -5.
[tex]\[
x = \frac{11}{5}
\][/tex]
### Conclusion:
Both reductions for Val's equation and Tia's equation lead to the same solution, [tex]\(x = \frac{11}{5}\)[/tex]. Therefore:
Both Val and Tia are correct.
