Question

How do you solve \[3x+2\le 5(x-4)\]?

Answer 1

Hint: We are given an expression which we have to solve for \[x\]. We will first open the brackets in the RHS. We will then separate the term with \[x\] and the terms without the \[x\] or the constants. And then we will write an expression in terms of \[x\] and get its value.

Complete step by step answer:
According to the given question, we are given a linear inequality which we have to solve for \[x\].
We will begin by writing the given expression, we have,
\[3x+2\le 5(x-4)\]----(1)
In equation (1), we can see that in the RHS there is a bracket. So, we will first simplify the equation, that is, we will open up the brackets.
So, 5 will be multiplied by \[x\] to give \[5x\] and with \[4\] we will get \[20\].
 We get the expression as,
\[\Rightarrow 3x+2\le 5x-5(4)\]
\[\Rightarrow 3x+2\le 5x-20\]---(2)
Now, we will have to separate the terms with \[x\] in it and the constant terms. So, we will take \[x\] terms on one side and the constants on the other side.
So, to the equation (2), we will be subtracting \[3x\] on both the sides of the inequality. We now get,
\[\Rightarrow 3x+2-3x\le 5x-20-3x\]
We can see that in the LHS, the \[3x\] gets cancelled and in the RHS \[3x\] is subtracted.
On solving further, we get the new expression as,
\[\Rightarrow 2\le 2x-20\]
Now, we will add 20 to both side of the inequality, we will have,
\[\Rightarrow 2+20\le 2x-20+20\]
On solving, we get the expression as,
\[\Rightarrow 22\le 2x\]
Dividing the above equation by 2, we will the expression in terms of \[x\], we have
\[\Rightarrow x\ge 11\]

Therefore, the value of \[x\ge 11\].

Note: The value that we obtained can be confirmed by substituting it in the given inequality. And we can see that the answer is correct. Also, while moving across the inequality, make note of the sign of the terms and accordingly the direction of the inequality will also change.