Answer :
Sure, let's solve the inequality [tex]\( 8x - 1 > 3x + 14 \)[/tex] step-by-step:
1. Isolate the [tex]\( x \)[/tex] terms on one side:
To achieve this, we'll first subtract [tex]\( 3x \)[/tex] from both sides of the inequality:
[tex]\[ 8x - 1 - 3x > 3x + 14 - 3x \][/tex]
[tex]\[ 5x - 1 > 14 \][/tex]
2. Isolate the constant term on the other side:
Next, we'll add 1 to both sides to move the constant term:
[tex]\[ 5x - 1 + 1 > 14 + 1 \][/tex]
[tex]\[ 5x > 15 \][/tex]
3. Solve for [tex]\( x \)[/tex]:
Finally, we'll divide both sides of the inequality by 5:
[tex]\[ \frac{5x}{5} > \frac{15}{5} \][/tex]
[tex]\[ x > 3 \][/tex]
Hence, the solution set for the inequality [tex]\( 8x - 1 > 3x + 14 \)[/tex] is [tex]\( x > 3 \)[/tex]. Given the options, none of them seem to exactly match. However, the correct solution derived here is [tex]\( x > 3 \)[/tex]. Double-check the given options for any possible matches or corrections.
1. Isolate the [tex]\( x \)[/tex] terms on one side:
To achieve this, we'll first subtract [tex]\( 3x \)[/tex] from both sides of the inequality:
[tex]\[ 8x - 1 - 3x > 3x + 14 - 3x \][/tex]
[tex]\[ 5x - 1 > 14 \][/tex]
2. Isolate the constant term on the other side:
Next, we'll add 1 to both sides to move the constant term:
[tex]\[ 5x - 1 + 1 > 14 + 1 \][/tex]
[tex]\[ 5x > 15 \][/tex]
3. Solve for [tex]\( x \)[/tex]:
Finally, we'll divide both sides of the inequality by 5:
[tex]\[ \frac{5x}{5} > \frac{15}{5} \][/tex]
[tex]\[ x > 3 \][/tex]
Hence, the solution set for the inequality [tex]\( 8x - 1 > 3x + 14 \)[/tex] is [tex]\( x > 3 \)[/tex]. Given the options, none of them seem to exactly match. However, the correct solution derived here is [tex]\( x > 3 \)[/tex]. Double-check the given options for any possible matches or corrections.
