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Rewrite the inequality in simplest form so that the coefficient of [tex]$x^2$[/tex] is positive and the right side is 0.

Drag the numbers and symbols to the correct locations on the inequality. Each number or symbol can be used more than once, but not all numbers and symbols will be used.

[tex]\(\square\)[/tex]

Sagot :

GinnyAnsweridn
Certainly! Let's solve the problem step by step. The goal is to rewrite the equation with a positive coefficient for [tex]\( x^2 \)[/tex] on the left side and zero on the right side.

Given the inequality:

[tex]\[ 3x^2 - 5x + 7 < 2x^2 - 3x + 8 \][/tex]

First, let's move all the terms to one side of the inequality so that the right side becomes zero. We subtract the expression on the right from the expression on the left:

[tex]\[ 3x^2 - 5x + 7 - (2x^2 - 3x + 8) < 0 \][/tex]

Now, distribute the negative sign through the parentheses:

[tex]\[ 3x^2 - 5x + 7 - 2x^2 + 3x - 8 < 0 \][/tex]

Next, combine like terms:

[tex]\[ (3x^2 - 2x^2) + (-5x + 3x) + (7 - 8) < 0 \][/tex]

Simplify the terms inside the parentheses:

[tex]\[ x^2 - 2x - 1 < 0 \][/tex]

So the simplified form of the inequality, with the coefficient of [tex]\( x^2 \)[/tex] being positive and the right side being zero, is:

[tex]\[ x^2 - 2x - 1 < 0 \][/tex]
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