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Solve the inequality 4x - 7 >= (-12x + 14) / 4

Solve The Inequality 4x 7 Gt 12x 14 4 class=

Sagot :

As given by the question:

There are given that the inequality:

[tex]4x-7\ge\frac{-12x+14}{4}[/tex]

Now,

Multiply both sides by 4:

[tex]\begin{gathered} 4x-7\ge\frac{-12x+14}{4} \\ (4x-7)\times4\ge\frac{-12x+14}{4}\times4 \\ (4x-7)\times4\ge-12x+14 \\ 16x-28\ge-12x+14 \end{gathered}[/tex]

Then,

Add 28 to both sides in the above equation:

[tex]\begin{gathered} 16x-28\ge-12x+14 \\ 16x-28+28\ge-12x+14+28 \\ 16x\ge-12x+42 \end{gathered}[/tex]

Then,

Add 12x to both sides in the above equation:

[tex]\begin{gathered} 16x\ge-12x+42 \\ 16x+12x\ge-12x+42+12x \\ 28x\ge42 \end{gathered}[/tex]

Then,

Divide both sides by 28:

[tex]\begin{gathered} 28x\ge42 \\ \frac{28x}{28}\ge\frac{42}{28} \\ x\ge\frac{3}{2} \end{gathered}[/tex]

Hence, the value of the given inequality is shown below:

[tex]x\ge\frac{3}{2}[/tex]

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