Question

if \: x = n \: find \: the \: solution \: of \: \frac{ - 3}{8} \leqslant \frac{3}{4} - \frac{x}{2}ifx=nfindthesolutionof 8 −3 ⩽ 4 3 − 2 x​

Answer 1

Answer:

13x−5<15x+4<7x+12

⇒ 15x+4>13x−5 and 15x+4<7x+12

⇒ 15x−13x>−5−4⇒15x−7x<12−4

⇒ 2x>−9⇒8x<8

⇒ x>

2

−9

⇒x<1

Solution : {x:

2

−9

<x<1,x∈R}

Answer 2

Answer:

A linear inequality is similar to a linear equation in that the largest exponent of a variable is 1. The following are examples of linear inequalities.

2x+22−x3x+143x−6≤1≥2<7x+2

The methods used to solve linear inequalities are similar to those used to solve linear equations. The only difference occurs when there is a multiplication or a division that involves a minus sign. For example, we know that 8>6. If both sides of the inequality are divided by −2, then we get −4>−3, which is not true. Therefore, the inequality sign must be switched around, giving −4<−3.

In order to compare an inequality to a normal equation, we shall solve an equation first.

Solve 2x+2=1:

2x+22x2xx=1=1−2=−1=−12

If we represent this answer on a number line, we get:

e9d9f02eff5609e47db4711862fbcf19.png

Now let us solve for x in the inequality 2x+2≤1:

2x+22x2xx≤1≤1−2≤−1≤−12

If we represent this answer on a number line, we get:

5c04492bb6bd71a23bf7cb3d4e1b5761.png

We see that for the equation there is only a single value of x for which the equation is true. However, for the inequality, there is a range of values for which the inequality is true. This is the main difference between an equation and an inequality.

Remember: when we divide or multiply both sides of an inequality by a negative number, the direction of the inequality changes. For example, if x<1, then −x>−1. Also note that we cannot divide or multiply by a variable.

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Step-by-step explanation:

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