solve the compound inequality. 4x+15 ≥-9 and 8x-6 ≤ 34

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apocritia apocritia · Answer 1 · 2018-08-19T06:32:49+02:00

Solution :

Given, compound inequality, [tex] 4x+15 \geq - 9 [/tex] and [tex] 8x-6 \leq 34 [/tex] .

Let us solve the first inequality for x

[tex] 4x+15 \geq - 9\\\Rightarrow 4x\geq -9-15\\\Rightarrow 4x\geq -24\\\Rightarrow x\geq\frac{-24}{4} \\\Rightarrow x\geq -6 [/tex]

Now, on solving the second inequality for x, we get

[tex] 8x-6\leq 34\\ => 8x\leq 34 +6\\=> 8x\leq 40\\=> x\leq \frac{40}{8} \\=> x\leq 5 [/tex]

Hence, the Solution of compound inequality can be expressed as [tex] -6 \leq x\leq 5 [/tex]

deepakrai138 deepakrai138 · Answer 2 · 2021-12-22T14:01:00+01:00

On solving, the result is [tex]-6\leq x\leq 5[/tex].

Given inequalities, [tex]4x+15\geq -9[/tex] and [tex]8x-6\leq 34[/tex].

Here [tex]4x+15\geq -9[/tex]

[tex]4x\geq -9-15\\4x\geq -24[/tex]

[tex]x\geq \frac{-24}{4} \\x\geq -6[/tex]

On solving first inequalities we conclude that the value of x is always greater than equals to -6.

[tex]now 8x-6\leq 34\\\\8x\leq 34+6\\\\8x\leq 40\\\\x\leq \frac{40}{8} \\\\x\leq 5[/tex]

So finally on resolving second inequality we conclude that the value of x is always less than equals to 5.

On resolving above inequalities we conclude that x have any value from -6 to 5.

Hence we have [tex]-6\leq x\leq 5[/tex].

For more details on inequalities follow the link below:

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