Advertisements
Advertisements
Question
Solve for x, the inequality given below.
|x − 1| ≤ 5, |x| ≥ 2
Solution
x – 1| ≤ 5
There are two cases,
x – 1 ≤ 5
Adding 1 to L.H.S. and R.H.S
⇒ x ≤ 6
⇒ –(x – 1) ≤ 5
⇒ –x + 1 ≤ 5
Subtracting 1 from L.H.S. and R.H.S.,
⇒ –x ≤ 4
⇒ x ≥ –4
From cases 1 and 2, we have
⇒ –4 ≤ x ≤ 6 ......[i]
Also,
|x| ≥ 2
⇒ x ≥ 2 and
⇒ – x ≥ 2
⇒ x ≤ –2
⇒ x ∈ (`oo`, –2] ∪ [2, `oo`) ......[ii]
Combining equation [i] and [ii], we get
x ∈ [–4, –2] ∪ [2, 6]
APPEARS IN
RELATED QUESTIONS
Solve: 12x < 50, when x ∈ R
Solve: −4x > 30, when x ∈ R
Solve: 4x − 2 < 8, when x ∈ N
3x − 7 > x + 1
3x + 9 ≥ −x + 19
\[\frac{x}{5} < \frac{3x - 2}{4} - \frac{5x - 3}{5}\]
\[x - 2 \leq \frac{5x + 8}{3}\]
\[\frac{2x - 3}{3x - 7} > 0\]
\[\frac{5x + 8}{4 - x} < 2\]
Solve each of the following system of equations in R.
1. x + 3 > 0, 2x < 14
Solve each of the following system of equations in R.
3x − 1 ≥ 5, x + 2 > −1
Solve each of the following system of equations in R.
11 − 5x > −4, 4x + 13 ≤ −11
Solve
\[\left| 4 - x \right| + 1 < 3\]
Solve
\[\left| \frac{2x - 1}{x - 1} \right| > 2\]
Solve \[\frac{\left| x - 2 \right| - 1}{\left| x - 2 \right| - 2} \leq 0\]
Mark the correct alternative in each of the following:
If − 3x\[+\]17\[< -\]13, then
Mark the correct alternative in each of the following:
If \[\left| x + 3 \right|\]\[\geq\]10, then
Solve the inequality, 3x – 5 < x + 7, when x is a natural number.
Solve `(x - 2)/(x + 5) > 2`.
Solve for x, |x + 1| + |x| > 3.
Solve the following system of inequalities:
`x/(2x + 1) ≥ 1/4, (6x)/(4x - 1) < 1/2`
If –x ≤ –4, then 2x ______ 8.
A solution of 9% acid is to be diluted by adding 3% acid solution to it. The resulting mixture is to be more than 5% but less than 7% acid. If there is 460 litres of the 9% solution, how many litres of 3% solution will have to be added?
If x < 5, then ______.
x and b are real numbers. If b > 0 and |x| > b, then ______.
If |x − 1| > 5, then ______.
If |x + 2| ≤ 9, then ______.
If x > y and z < 0, then – xz ______ – yz.
