Algebra 1

Solving Compound Inequalities

-25 ≤ -5n ≤ 30

Let's solve one side of the inequality at a time.

-5n ≤ 30

Divide both sides by -5. When you divide by a negative number, it switches the sign.

n ≥ -6

Now, let's do the other side of the inequality.

-5n ≥ -25

Divide both sides by -5.

n ≤ 5

Our new compound inequality looks like: -6 ≤ n ≤ 5

Put one point at -6 and one point at 5 and connect the dots to graph the inequality.

-1, -2, -3, -4, -6

step-by-step explanation:

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions