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In $3-14,$ write the solution set of each equation.$$|-5 a|+7=22$$

$a=\pm 3$

Algebra

Chapter 1

THE INTEGERS

Section 4

Solving Absolute Value Equations and Inequalities

The Integers

Equations and Inequalities

Polynomials

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Lectures

01:32

In mathematics, the absolu…

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In $3-14,$ write the solut…

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Find the solution set for …

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Solve each equation. $$a+7…

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Solve each equation.$\…

okay. To solve this absolute value equation, we first need to isolate the absolute value. And we can do that by subtracting seven on both sides. So 22 minus seven is 15. So I have minus five day and the absolute values is equal to 15. And now I need to split that into two separate equations. So I have minus five is equal to 15 minus five is equal to minus 15 as well. So when I solve here to divide by minus five, I'm going to get a Z equals minus three and same thing here, denied by minus five. And here again, a is equal. Positive three. Now we have to check. So if I check here with my minus three minus five times minus three in the absolute value is 15 15 plus seven is 22. So this works. And then for a equals three, it's also going to work. It's minus five times three is minus 15. Absolute value of it makes it 15 15 plus seven is 22. So both of these solutions work. And here's your sort of solutions

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