Question

How do you solve 2x-1 < 7?

Answer 1

Hint: In this question, we are given an inequality in terms of x and we need to solve it to find the inequality of x i.e. we need to find if x>c or xc or x
Complete step-by-step answer:
Here we are given the inequality as 2x-1 < 7.
We have to solve this inequality such that we can find if x is greater than or less than any constant. We can say that, we need to find the interval of x which will satisfy this inequality. For this, let us add, subtract, multiply and divide some terms on both sides of the inequality to get either x>c or xWe have 2x-1 < 7.
As we can see here is an unwanted constant 1 on the left side. So let us remove it. For removing let us add 1 to both sides of the inequality we get 2x-1+1 < 7+1.
Adding and subtracting the terms we get 2x < 8.
Since x still has a coefficient as 2 which is not required. So let us remove it. For removing the coefficient let us divide both sides of the inequality by 2 we get $\dfrac{2x}{2}\text{ }<\text{ }\dfrac{8}{2}$.
2 divided by 2 gives us 1 and 8 divided by 2 gives us 4 so we get x < 4.
Hence we have found inequality of form x < c.
So this is our final answer.
Solving 2x-1 < 7 we get x < 4.

Note: Students should take care of the signs while adding, subtracting the terms. Note that, all numbers less than 4 as x will satisfy the inequality 2x-1 < 7. For example, for x = 3 which is less than 4 we have 2(3)-1 < 7 = 6-1 < 7 = 5 < 7. We know 5 is less than 7 therefore for x = 3 the inequality holds.