Question

Solve the inequality:
4-3x<16

Answer 1

x > -4

Explanation:

This is solved just like as if it was an equation. Its a two-step equation (inequality) The only thing that's different is with an inequality, it is imperative that you flip the inequality symbol if you multiply or divide by a negative number.

Here, we'll subtract 4 from both sides. Then divide by -3 on both sides. Flip! the < to a >.

see image.

Answer 2

x > -4.

Explanation:

1. Write the expression.

`4-3x < 16`

2. Subtract "4" from both sides of the equation.

`4-3x-4 < 16-4\\ \\-3x < 12`

3. Divide both sides by "-3" and switch the inequality symbol.

`(-3x)/(-3) < (12)/(-3) \\ \\x > -4`

Important. See that we switched the inequality symbol from "<" to ">", and this is because the symbol of the coefficient of variable "x" changed from negative to positive when it was divided by "-3". This rule will always be true, any time the symbol of the variable changed, the inequality symbol changes.

4. Verify.

If x >-4 is the correct answer, then substituting x by "-4" in the inequation should make the inequation return the same value on both sides of the inequality symbol (>).

`4-3(-4) > 16\\ \\4-(-12) > 16\\ \\4+12 > 16\\ \\16 > 16`

That's correct! x > -4 is the correct answer.