Advertisements
Advertisements
प्रश्न
Solve for x, the inequality given below.
`-5 ≤ (2 - 3x)/4 ≤ 9`
उत्तर
`-5 ≤ (2 - 3x)/4 ≤ 9`
Multiplying each term by 4, we get
⇒ –20 ≤ 2 – 3x ≤ 36
Adding –2 each term, we get
⇒ –22 ≤ –3x ≤ 34
Dividing each term by 3, we get
⇒ `-22/3` ≤ –x ≤ `34/3`
We know that,
Multiplication by –1 inverts the inequality.
So, multiplying each term by –1, we get
⇒ `(-34)/3` ≤ x ≤ `22/3`
APPEARS IN
संबंधित प्रश्न
Solve: 12x < 50, when x ∈ Z
x + 5 > 4x − 10
\[\frac{3x - 2}{5} \leq \frac{4x - 3}{2}\]
\[\frac{x}{5} < \frac{3x - 2}{4} - \frac{5x - 3}{5}\]
\[\frac{2\left( x - 1 \right)}{5} \leq \frac{3\left( 2 + x \right)}{7}\]
\[\frac{x - 1}{3} + 4 < \frac{x - 5}{5} - 2\]
\[\frac{2x + 3}{4} - 3 < \frac{x - 4}{3} - 2\]
\[\frac{4 + 2x}{3} \geq \frac{x}{2} - 3\]
\[\frac{6x - 5}{4x + 1} < 0\]
\[\frac{2x - 3}{3x - 7} > 0\]
\[\frac{5x + 8}{4 - x} < 2\]
Solve the following system of equation in R.
x + 5 > 2(x + 1), 2 − x < 3 (x + 2)
Solve each of the following system of equations in R.
20. −5 < 2x − 3 < 5
Solve \[\frac{\left| x - 2 \right|}{x - 2} > 0\]
Solve \[\frac{\left| x - 2 \right| - 1}{\left| x - 2 \right| - 2} \leq 0\]
Solve \[\frac{1}{\left| x \right| - 3} \leq \frac{1}{2}\]
Solve \[1 \leq \left| x - 2 \right| \leq 3\]
Mark the correct alternative in each of the following:
If − 3x\[+\]17\[< -\]13, then
Mark the correct alternative in each of the following:
The inequality representing the following graph is
Solve the inequality, 3x – 5 < x + 7, when x is a natural number.
Solve the inequality, 3x – 5 < x + 7, when x is a real number.
Solve the following system of inequalities:
`x/(2x + 1) ≥ 1/4, (6x)/(4x - 1) < 1/2`
If x ≥ –3, then x + 5 ______ 2.
If –x ≤ –4, then 2x ______ 8.
Solve for x, the inequality given below.
4x + 3 ≥ 2x + 17, 3x – 5 < –2
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?
In drilling world’s deepest hole it was found that the temperature T in degree celcius, x km below the earth’s surface was given by T = 30 + 25(x – 3), 3 ≤ x ≤ 15. At what depth will the temperature be between 155°C and 205°C?
If x is a real number and |x| < 3, then ______.
If |x − 1| > 5, then ______.
