Solve the following inequation, write the solution set and represent it on the number line.
$- 3 (x - 7) \geq 15 - 7 x > \frac{x + 1}{3}, x ϵ R$
[3 MARKS]

Open in App

Solution

Solving each inequation: 1 Mark each
Solution on number line: 1 Mark

$G i v e n - 3 (x - 7) \geq 15 - 7 x > \frac{x + 1}{3}, x ϵ R \Rightarrow - 3 x + 7 x \geq 15 - 21 \Rightarrow 4 x \geq - 6 \Rightarrow x \geq - \frac{3}{2} 15 - 7 x > \frac{x + 1}{3} \Rightarrow 45 - 21 x > x + 1 \Rightarrow - 21 x - x > 1 - 45 \Rightarrow - 22 x > - 44 \Rightarrow x < 2$
$∴ S o l u t i o n s e t = {x : x ϵ R, - \frac{3}{2} \leq x < 2}$

Suggest Corrections

Similar questions

Q. Solve the following inequation, write the solution set and represent it on the number line.

- 3 (x - 7) \geq 15 - 7 x > \frac{x + 1}{3}, x \in R

Write the solution set and its representation on the number line for the following inequation.
$\frac{x + 1}{3} < 15 - 7 x \leq - 3 (x - 7); x \in R .$

Q. Solve the following inequation and write the solution set :

13 x - 5 < 15 x + 4 < 7 x + 12, x ϵ R

Represent the solution on a real number line.
[3 MARKS]

Q. Solve the following inequation and represent the solution set on the number line:

- 2 \frac{2}{3} \leq x + \frac{1}{3} < 3 \frac{1}{3}, x ϵ R

.
[4 MARKS]

Q. Solve the following inequation, write the solution set and represent it on the number line:

- \frac{x}{3} \leq \frac{x}{2} - 1 \frac{1}{3} < \frac{1}{6}, x \in R

Join BYJU'S Learning Program

Solve the following inequation, write the solution set and represent it on the number line. −3(x−7)≥15−7x>x+13,xϵR [3 MARKS]

Solving each inequation: 1 Mark each Solution on number line: 1 Mark Given−3(x−7)≥15−7x>x+13,xϵR⇒−3x+7x≥15−21⇒4x≥−6⇒x≥−3215−7x>x+13⇒45−21x>x+1⇒−21x−x>1−45⇒−22x>−44⇒x<2 ∴Solution set={x:xϵR,−32≤x<2}

Solve the following inequation, write the solution set and represent it on the number line.
$- 3 (x - 7) \geq 15 - 7 x > \frac{x + 1}{3}, x ϵ R$
[3 MARKS]