Question Solve for $x$ in the equation $-14x - 26 = \frac{-7}{8}(16x - 6)$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $-14x - 26 = \frac{-7}{8}(16x - 6)$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we need to distribute the fraction $\frac{-7}{8}$ across the terms inside the parentheses on the right side of the equation.
$-14x - 26 = \frac{-7}{8} \cdot 16x - \frac{-7}{8} \cdot (-6)$

STEP 3

Multiply the fraction $\frac{-7}{8}$ by each term inside the parentheses.
$-14x - 26 = \frac{-7}{8} \cdot 16x + \frac{7}{8} \cdot 6$

STEP 4

Simplify the multiplication by reducing the fractions where possible.
$-14x - 26 = -14x + \frac{7}{8} \cdot 6$

STEP 5

Calculate the product of $\frac{7}{8}$ and $6$ .
$\frac{7}{8} \cdot 6 = \frac{7 \cdot 6}{8}$

STEP 6

Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
$\frac{7 \cdot 6}{8} = \frac{42}{8} = \frac{21}{4}$

STEP 7

Substitute the reduced fraction back into the equation.
$-14x - 26 = -14x + \frac{21}{4}$

STEP 8

Since $-14x$ appears on both sides of the equation, we can add $14x$ to both sides to eliminate the $x$ terms.
$-14x + 14x - 26 = -14x + 14x + \frac{21}{4}$

STEP 9

Simplify both sides of the equation.
$-26 = \frac{21}{4}$

STEP 10

To solve for $x$ , we need to isolate $x$ on one side of the equation. However, since the $x$ terms have been eliminated, we see that the equation has no solution for $x$ because the remaining equation $-26 = \frac{21}{4}$ is not true for any value of $x$ . This means the equation is inconsistent and there is no solution.
The equation $-14x - 26 = \frac{-7}{8}(16x - 6)$ has no solution.

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