Generate questions to solve based on inequality csca style

Mathematics

ScanSolve AI Answer

Answer

C

x<6x < 6

Step-by-step solution

7 steps

Here are some inequality problems in a multiple-choice format, similar to what you might see in an exam. I'll solve each one step-by-step.


Part 1· 2 steps

Solve the inequality for xx:

3x−8<103x - 8 < 10

A) x<2x < 2
B) x>2x > 2
C) x<6x < 6
D) x>6x > 6

  1. Add 8 to both sides of the inequality to isolate the term with xx.

    3x−8+8<10+83x - 8 + 8 < 10 + 8 3x<183x < 18
  2. Divide both sides by 3.

    Since 3 is a positive number, the inequality sign remains the same.

    3x3<183\frac{3x}{3} < \frac{18}{3} x<6x < 6

    The correct option is C) x<6x < 6.


Part 2· 2 steps

Solve the inequality for yy:

−2y+5≥15-2y + 5 \ge 15

A) y≥−5y \ge -5
B) y≤−5y \le -5
C) y≥10y \ge 10
D) y≤10y \le 10

  1. Subtract 5 from both sides of the inequality.

    −2y+5−5≥15−5-2y + 5 - 5 \ge 15 - 5 −2y≥10-2y \ge 10
  2. Divide both sides by -2.

    Since -2 is a negative number, you must reverse the direction of the inequality sign.

    −2y−2≤10−2\frac{-2y}{-2} \le \frac{10}{-2} y≤−5y \le -5

    The correct option is B) y≤−5y \le -5.


Part 3· 3 steps

Solve the inequality for zz:

5z−4≤2z+115z - 4 \le 2z + 11

A) z≤5z \le 5
B) z≥5z \ge 5
C) z≤73z \le \frac{7}{3}
D) z≥73z \ge \frac{7}{3}

  1. Subtract 2z2z from both sides to gather the zz terms on one side.

    5z−4−2z≤2z+11−2z5z - 4 - 2z \le 2z + 11 - 2z 3z−4≤113z - 4 \le 11
  2. Add 4 to both sides to isolate the term with zz.

    3z−4+4≤11+43z - 4 + 4 \le 11 + 4 3z≤153z \le 15
  3. Divide both sides by 3.

    Since 3 is a positive number, the inequality sign remains the same.

    3z3≤153\frac{3z}{3} \le \frac{15}{3} z≤5z \le 5

    The correct option is A) z≤5z \le 5.


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