Certainly! Let's break down the solution step-by-step.
Part A: Solve the equation [tex]\(5 + x - 14 = x - 7\)[/tex]
1. Start with the given equation:
[tex]\[ 5 + x - 14 = x - 7 \][/tex]
2. Simplify both sides of the equation:
[tex]\[ 5 - 14 + x = x - 7 \][/tex]
[tex]\[ -9 + x = x - 7 \][/tex]
3. Notice that [tex]\(x\)[/tex] appears on both sides of the equation.
4. Subtract [tex]\(x\)[/tex] from both sides to eliminate [tex]\(x\)[/tex]:
[tex]\[ -9 + x - x = x - 7 - x \][/tex]
[tex]\[ -9 = -7 \][/tex]
5. Now we have [tex]\(-9 = -7\)[/tex], which is a contradiction.
Thus, no value for [tex]\(x\)[/tex] can make this equation true. Therefore, there is no solution to the equation.
Part B: Use the values [tex]\(x = -2, 0, 3\)[/tex] to verify the solution
To verify that there is indeed no solution, we will substitute each of the provided values of [tex]\(x\)[/tex] into the original equation and check whether the left side equals the right side.
1. For [tex]\(x = -2\)[/tex]:
[tex]\[
\text{Left side} = 5 + (-2) - 14 = 5 - 2 - 14 = -11 \\
\text{Right side} = -2 - 7 = -9
\][/tex]
Since [tex]\(-11 \neq -9\)[/tex], the equation does not hold true for [tex]\(x = -2\)[/tex].
2. For [tex]\(x = 0\)[/tex]:
[tex]\[
\text{Left side} = 5 + 0 - 14 = 5 - 14 = -9 \\
\text{Right side} = 0 - 7 = -7
\][/tex]
Since [tex]\(-9 \neq -7\)[/tex], the equation does not hold true for [tex]\(x = 0\)[/tex].
3. For [tex]\(x = 3\)[/tex]:
[tex]\[
\text{Left side} = 5 + 3 - 14 = 8 - 14 = -6 \\
\text{Right side} = 3 - 7 = -4
\][/tex]
Since [tex]\(-6 \neq -4\)[/tex], the equation does not hold true for [tex]\(x = 3\)[/tex].
In conclusion, verifying the equation with the values [tex]\(x = -2, 0, 3\)[/tex] shows that in each case, the left side does not equal the right side, confirming that there is indeed no solution to the equation [tex]\(5 + x - 14 = x - 7\)[/tex].
