H/w ar \( x-z<2 x+5 \) क- \( -4 x+1 \leqslant 2 \) को \( -2 x+3>10 \) aet the velue of \( x \)

To solve the inequalities step by step, we will address each inequality one by one. ### 1. Solve the first inequality: \[ x - z < 2x + 5 \] Rearranging the inequality: \[ x - 2x < 5 + z \] \[ -x < 5 + z \] Multiplying both sides by -1 (remember to reverse the inequality): \[ x > -5 - z \] ### 2. Solve the second inequality: \[ -4x + 1 \leq 2 \] Rearranging the inequality: \[ -4x \leq 2 - 1 \] \[ -4x \leq 1 \] Dividing both sides by -4 (again, reverse the inequality): \[ x \geq -\frac{1}{4} \] ### 3. Solve the third inequality: \[ -2x + 3 > 10 \] Rearranging the inequality: \[ -2x > 10 - 3 \] \[ -2x > 7 \] Dividing both sides by -2 (reverse the inequality): \[ x < -\frac{7}{2} \] ### Summary of the inequalities: 1. \( x > -5 - z \) 2. \( x \geq -\frac{1}{4} \) 3. \( x < -\frac{7}{2} \) Now, we need to find the values of \( x \) that satisfy all three inequalities. ### Finding the intersection: - From the second inequality, \( x \geq -\frac{1}{4} \). - From the third inequality, \( x < -\frac{7}{2} \) which is approximately -3.5. Since \( -\frac{1}{4} \) (which is 0.25) is greater than -3.5, there are no values of \( x \) that can satisfy all three inequalities simultaneously. ### Conclusion: There are no values of \( x \) that satisfy all the given inequalities.