Cumulative Assessment
Sign In
Simplify each inequality and compare.
| 3x+6≤8+2x | 5x-5≥7x-9 | -2-3/2x≥-3-x |
We have been given four inequalities and were asked to determine which ones are equivalent. The easiest way to do this is by simplifying all of them and comparing the results. Let's look at these one at a time.
To simplify the first inequality, we need to utilize the Subtraction Property of Inequalities.
To simplify the second inequality, we need to remember that dividing by a negative number requires us to reverse the direction of the inequality sign.
LHS+5≥RHS+5
LHS-7x≥RHS-7x
Divide by -2 and flip inequality sign
To simplify the third inequality, we need to remember that dividing by a negative number requires us to reverse the direction of the inequality sign.
To simplify the fourth inequality, we can make it a bit easier if we multiply everything by -2 first. This will eliminate the fraction and all of the negatives.
Multiply by -2 and flip inequality sign
LHS-4≤RHS-4
LHS-2x≤RHS-2x
Now, we can compare the results. 3x+6≤8+2x& ⇒ x≤2 [0.7em] 5x-5≥7x-9& ⇒ x≤2 [0.7em] 12-3x≤18& ⇒ x≥-2 [0.2em] -2- 32x≥-3-x& ⇒ x≤2 The first, second, and fourth inequalities are equivalent.