Question

6-26. solve for ( x ). check your solutions, if possible. graph your solutions on a number line. homework help
( \text{a. } -2(4 - 3x) - 6x = 10 )
( \text{b. } \frac{x - 5}{-2} = \frac{x - 1}{-3} )

Explanation:

Part a

Step1: Expand the left side

$-2(4-3x)-6x = -8 + 6x - 6x$

Step2: Simplify the expression

$-8 + (6x - 6x) = -8$

Step3: Compare to right side

$-8
eq 10$, so no solution exists.

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Part b

Step1: Cross-multiply to eliminate fractions

$-3(x-8) = 2(x-1)$

Step2: Expand both sides

$-3x + 24 = 2x - 2$

Step3: Isolate $x$ terms

$-3x - 2x = -2 - 24$

Step4: Simplify and solve for $x$

$-5x = -26$
$x = \frac{-26}{-5} = \frac{26}{5} = 5.2$

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Graphing on a number line:

• For part a: Draw a blank number line, as there are no values of $x$ that satisfy the equation.
• For part b: Draw a number line, place a closed dot at $5.2$ (or $\frac{26}{5}$) to represent the solution.

Answer:

No solution