Question

What value of “a” would make the equation have no solution?

4(5x+1) = -2(ax+4)

Answer 1

Answer: a = -10

Concept:

When an equation has no solution, in most cases, it means that the variables are being canceled out, and left with unequal constants.

For example:

                                             2x + 3 = 2 +2x

The 2x can be canceled out on both sides, which left us with:

                                                     3 = 2

3 does not equal to 2, therefore, it has no solution

Solve:

Given equation

4 (5x + 1) = -2 (ax + 4)

Expand the parenthesis

4 (5x) + 4 (1) = -2 (ax) + (-2) (4)

20x + 4 = -2ax - 8

According to the concept, we need to make the variables equal to cancel them out and left with unequal constants

20x = -2ax

Divide x on both sides

20x / x = -2ax / x

20 = -2a

Divide -2 on both sides

20 / -2 = -2a / -2

$\Large\boxed{a=-10}$

Hope this helps!! :)

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