Question

Solve the following equation: |-3x+3|-9=12

Answer 1

`\large\boxed{\left \{ {{x\: = \: 8} \atop {x\: =\: -6}} \right. }\\`

Explanation:

`\left| -3x+3 \right| -9=12`

At first, let's add - 9 to both the sides. So,

`\left| -3x+3 \right| -9=12\\|-3x+3|=21`

Now, using the definition of absolute value, we can change the equation to..

`-3x+3=21 \\-3x+3=-21`

By, subtracting 3 from both the sides,

`-3x=18 \\-3x=-24`

Now, divide both the sides by 6,

`x=-6 \\x=8`

We now have 2 values of x. They are...

`\large\boxed{\left \{ {{x\: = \: 8} \atop {x\: =\: -6}} \right. }\\`

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Hope it helps!

`\mathfrak{Lucazz}`