Math - Solving Inequalities

1

Solve for :

$5-3x\leq14$

$x\geq-3$

$x\geq3$

$x\geq9$

$x\leq3$

$x\geq0$

Explanation

Inequalities can be treated like any other equation except when multiplying and dividing by negative numbers. When multiplying or dividing by negative numbers, we just flip the sign of the inequality so that becomes , and vice versa.

$5-3x\leq14$

$-3x\leq9$

$\frac{-3x}{-3}\geq\frac{9}{-3}$

$x\geq-3$

2

Solve for :

$\frac{-7x-2}{3}>11$

Explanation

Inequalities can be treated like any other equation except when multiplying and dividing by negative numbers. When multiplying or dividing by negative numbers, we just flip the sign of the inequality so that becomes , and vice versa.

$\frac{-7x-2}{3}>11$

$\frac{-7x}{-7}<\frac{35}{-7}$

3

Solve the inequality for x:

Explanation

Subtract 4 from both sides:

Divide both sides by 2:

4

Solve for :

$9x-27\geq6x$

$x\geq9$

$x\leq9$

$x\geq3$

$x\leq3$

Explanation

$9x-27\geq6x$

Move like terms to the same sides:

$9x-6x\geq27$

Combine like terms:

$3x\geq27$

Divide both sides by 3:

$x\geq9$

5

Solve for :

$x<-6\ and\ x>2$

$x<-2\ and\ x>6$

Explanation

Inequalities can be treated like any other equation except when multiplying and dividing by negative numbers. When multiplying or dividing by negative numbers, we just flip the sign of the inequality so that becomes , and vice versa. When we solve binomials, we must take extra caution because .

So when we solve inequalities with binomials, we must create two scenarios: one where the value inside of the parentheses is positive and one where it is negative. For the negative scenario, we must flip the sign as we normally do for inequalities.

Now we must create our two scenarios:

$x+2>{\sqrt{16}}$ and $x+2<-{\sqrt{16}}$

Notice that in the negative scenario, we flipped the sign of the inequality.

and

6

Solve for :

$x>-2\ and\ x<12$

$x<5\ and\ x>10$

$x>0\ and\ x<2$

Explanation

Inequalities can be treated like any other equation except when multiplying and dividing by negative numbers. When multiplying or dividing by negative numbers, we just flip the sign of the inequality so that becomes , and vice versa. When we solve binomials, we must take extra caution because .

So when we solve inequalities with binomials, we must create two scenarios: one where the value inside of the parentheses is positive and one where it is negative. For the negative scenario, we must flip the sign as we normally do for inequalities.