Question

textless \ \frac{x+1}{4}" alt="2x+5\ \textless \ \frac{x+1}{4}" align="absmiddle" class="latex-formula">

Answer 1

$\boldsymbol{\sf{2x+5 < \dfrac{x+1}{4} }}$

Multiply the two sides of the equation by 4. Since 4 is > 0, the direction of inequality remains the same.

          $\boldsymbol{\sf{8x+20 < x+1 }}$

Resta x en los dos lados.

              $\boldsymbol{\sf{8x+20-x < 1 }}$

Combine 8x and −x to get 7x.

                $\boldsymbol{\sf{7x+20 < 1 }}$

Subtract 20 on both sides.

                 $\boldsymbol{\sf{7x < 1-20 \ \ \longmapsto \ \ [To \ subtract] }}$

                  $\boldsymbol{\sf{7x < -19 }}$

Divide the two sides by 7. Since 7 is >0, the direction of inequality remains the same.

                     $\boldsymbol{\sf{x < -\dfrac{19}{7} } }$

As the end result, it is not simplified or divided, then

                               $\blue{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ x < -\frac{19}{7} }}}}$

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Answer 2

Given :-

• 2x + 5 < x + 1 / 4

Solution :-

>> 2x + 5 < x + 1 / 4

>> 4 (2x + 5) < x + 1

>> 4 × (2x + 5) < x + 1

>> 8x + 20 < x + 1

>> 8x - x < 1 - 20

>> 7x < 1 - 20

>> 7x < -19

>> x = -19 / 7