Question

Write the solution interval of the inequality: 4(2x-1) -11 ≥ 7​

Answer 1

$\large\underline{\sf{Solution-}}$

Given inequality is

$\rm \: 4(2x - 1) - 11 \geqslant 7$

$\rm \: 8x - 4 - 11 \geqslant 7$

$\rm \: 8x - 15 \geqslant 7$

$\rm \: 8x \geqslant 7 + 15$

$\rm \: 8x \geqslant22$

$\rm \: x \geqslant \dfrac{22}{8}$

$\bf\implies \: x \geqslant \dfrac{11}{4}$

$\bf\implies \: x \: \in \: \bigg[ \dfrac{11}{4}, \: \infty \bigg)$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{ |x| < y\rm\implies \: - y < x < y}\\ \\ \bigstar \: \bf{ |x| \leqslant y\rm\implies \: - y \leqslant x \leqslant y}\\ \\ \bigstar \: \bf{ |x| > y\rm\implies \: x < - y \: or \: x > y} \: \\ \\ \bigstar \: \bf{ |x| \geqslant y\rm\implies \:x \leqslant - y \: or \: x \geqslant y}\\ \\ \bigstar \: \bf{ |x - a| < y\rm\implies \:a - y < x < a + y}\\ \\ \bigstar \: \bf{ |x - a| \leqslant y\rm\implies \:a - y \leqslant x \leqslant a + y}\\ \\ \end{array} }}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

Given,

$\bf 4(2x - 1) - 11 \geqslant 7$

write the solution of the given inequality

SOLUTION :-

$\tt⇢ \: \:4(2x - 1) - 11 \geqslant 7$

$\tt⇢ \: \:4 \times (2x - 1) \geqslant 7 + 11$

$\tt⇢ \: \:8x - 4 \geqslant 18$

$\tt⇢ \: \:8x \geqslant 18 + 4$

$\tt⇢ \: \:x \geqslant \frac{22}{8}$

$\tt⇢ \: \:x \geqslant \frac{11}{4}$

FINAL ANSWER :-

The solutions of the given inequality are

$\huge \bf x \in \huge{[ } {\frac{11}{4} , \infty} )$