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Determine whether the following statement is true or false.

If -5x ≤ 45, then 5x - 2 < 45.
Choose the correct answer below.
a. True
b. False

1 Answer

4 votes

Final answer:

The statement 'If -5x ≤ 45, then 5x - 2 < 45' is true. Upon solving the first inequality and substituting the values into the second inequality, every value of x that satisfies the first inequality also satisfies the second one.

Therefore, the original statement is true.

Step-by-step explanation:

The statement 'If -5x ≤ 45, then 5x - 2 < 45' is being analyzed to determine if it's true or false. Let's first solve the inequality -5x ≤ 45. When we divide each side by -5 (and remember to reverse the inequality sign because we are dividing by a negative number), we get x ≥ -9. Now, if we substitute x = -9 into the second inequality 5x - 2 < 45, we get 5(-9) - 2 < 45, which simplifies to -45 - 2 < 45, or -47 < 45, which is true.

However, since the first inequality states that x can be any value greater than or equal to -9, let's consider another value for x that is greater than -9, say x = 0. Substituting x = 0 into 5x - 2 < 45 gives us 0 - 2 < 45, or -2 < 45, which is also true. This means that for every x that satisfies the first inequality, the second inequality is also satisfied. Therefore, the original statement is true.

User Jordan Daniels
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