Question

indicate whether the value of x us a solution or not a solution of the inequality -9x - 4 ≤ 23. select the words from the drop-down list to correctly complete the sentence. x = 26 is a solution not a solution

Explanation:

Step1: Substitute \( x = 26 \) into the inequality

Substitute \( x = 26 \) into \( -9x - 4 \leq 23 \). First, calculate \( -9\times26 \). \( -9\times26=-234 \). Then subtract 4: \( -234 - 4=-238 \).

Step2: Check the inequality

Now we have \( -238 \leq 23 \). Since \( -238 \) is less than \( 23 \), but wait, wait, no—wait, the inequality is \( -9x - 4 \leq 23 \). Wait, let's re - calculate. Wait, \( -9x-4\leq23 \). Let's solve the inequality first to find the solution set. Add 4 to both sides: \( -9x\leq23 + 4=27 \). Then divide both sides by - 9 (remember to reverse the inequality sign when dividing by a negative number): \( x\geq - 3 \). Now, \( x = 26 \) is greater than \( - 3 \), but wait, when we substitute \( x = 26 \) into \( -9x-4 \), we get \( -9\times26-4=-234 - 4=-238 \). And \( -238\leq23 \) is true? Wait, no, \( -238 \) is much less than \( 23 \), so it should satisfy the inequality? Wait, maybe I made a mistake. Wait, the original problem is to check if \( x = 26 \) is a solution. Let's do the substitution again. \( -9\times26=-234 \), \( -234-4=-238 \). Is \( -238\leq23 \)? Yes, because any negative number is less than a positive number. But wait, maybe the inequality was written wrong? Wait, no, the user's problem is to check if \( x = 26 \) is a solution of \( -9x - 4\leq23 \). Wait, but let's solve the inequality properly. \( -9x-4\leq23 \). Add 4 to both sides: \( -9x\leq27 \). Divide both sides by - 9: \( x\geq - 3 \). Since \( 26\geq - 3 \), \( x = 26 \) should be a solution? But that contradicts the initial thought. Wait, maybe the inequality is \( -9x-4\geq23 \)? No, the user's problem says \( -9x - 4\leq23 \). Wait, maybe I misread. Wait, the image shows "the inequality \( -9x - 4\leq23 \)". So substituting \( x = 26 \): \( -9(26)-4=-234 - 4=-238 \). \( -238\leq23 \) is true, so \( x = 26 \) is a solution? But the drop - down has "a solution" and "not a solution". Wait, maybe there is a typo in the inequality? Or maybe I made a mistake. Wait, let's check again. \( -9x-4\leq23 \). Let's solve for \( x \):

\( -9x\leq23 + 4=27 \)

\( x\geq - 3 \) (because we divide by - 9, reverse inequality)

Since \( 26\geq - 3 \), \( x = 26 \) is in the solution set, so it is a solution.

Wait, but maybe the original inequality was \( 9x - 4\leq23 \)? If it was \( 9x-4\leq23 \), then \( 9x\leq27 \), \( x\leq3 \). Then \( x = 26 \) would not be a solution. Maybe there was a sign error in the problem. But based on the given inequality \( -9x - 4\leq23 \), \( x = 26 \) is a solution.

Wait, but let's check the arithmetic again. \( -9\times26=-234 \), \( -234-4=-238 \). \( -238\leq23 \): yes, because \( -238 \) is less than \( 23 \). So \( x = 26 \) is a solution.

Answer:

a solution