Mathematics, 27.10.2020 23:40 Zarek2853

What is the solution to 8x - 3(2x - 4) = 3x - 18?

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Answer from: sydneykated

the answer is 3

Step-by-step explanation:

the answer is 3 implifying

8x + -3(2x + -4) = 18

Reorder the terms:

8x + -3(-4 + 2x) = 18

8x + (-4 * -3 + 2x * -3) = 18

8x + (12 + -6x) = 18

Reorder the terms:

12 + 8x + -6x = 18

Combine like terms: 8x + -6x = 2x

12 + 2x = 18

Solving

12 + 2x = 18

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-12' to each side of the equation.

12 + -12 + 2x = 18 + -12

Combine like terms: 12 + -12 = 0

0 + 2x = 18 + -12

2x = 18 + -12

Combine like terms: 18 + -12 = 6

2x = 6

Divide each side by '2'.

x = 3

Simplifying

x = 3

Answer from: Quest

i can you with this question sweetie!

step-by-step explanation:

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

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