Write down the range of values of x which satisfy both the inequalities

3x – 7 < 3 – x

x – 12 ≤3(x – 3)

A] 1.5 < x < 2.5

B] x > 1.5

C] -2.5 < x < 1.5

D] -1.5 ≤ x < 2.5

E] x < -1.5

Write down the range of values of x which satisfy both the inequalities

3x – 7 < 3 – x

x – 12 ≤3(x – 3)

A] 1.5 < x < 2.5

B] x > 1.5

C] -2.5 < x < 1.5

D] -1.5 ≤ x < 2.5

E] x < -1.5

Hi!

3x-7<3-x

4x<10–> x<2.5

X-12《 3x-9

-3《 2X → X 》-1.5

-1.5《 X <2.5

3 Likes

Hi!

For equation 1:

3x-7<3-x (adding +7 on both side of the equation)

3x<10-x (now adding +x on both sides)

4x<10

thus, x<2.5

For equation 2:

x-12 ≤ 3x-9 (adding +9 on both sides)

x-3 ≤ 3x (subtracting x from both sides)

-3 ≤ 2x

thus -1.5 ≤ x

therefore the range will be -1.5 ≤ x < 2.5

Hope this helps!

3 Likes