Let's solve the inequality step-by-step:
Given the inequality:
[tex]\[ 0.2(x + 20) - 3 > -7 - 6.2x \][/tex]
1. Use the distributive property:
[tex]\[ 0.2(x) + 0.2(20) - 3 > -7 - 6.2x \][/tex]
[tex]\[ 0.2x + 4 - 3 > -7 - 6.2x \][/tex]
[tex]\[ 0.2x + 1 > -7 - 6.2x \][/tex]
2. Combine like terms:
First, let's get all [tex]\(x\)[/tex] terms on one side and all constant terms on the other side:
[tex]\[ 0.2x + 6.2x + 1 > -7 \][/tex]
[tex]\[ 6.4x + 1 > -7 \][/tex]
3. Use the subtraction property of inequality:
Subtract 1 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ 6.4x + 1 - 1 > -7 - 1 \][/tex]
[tex]\[ 6.4x > -8 \][/tex]
4. Use the division property of inequality:
Divide both sides by 6.4 to solve for [tex]\(x\)[/tex]:
[tex]\[ \frac{6.4x}{6.4} > \frac{-8}{6.4} \][/tex]
[tex]\[ x > -1.25 \][/tex]
Therefore, the solution to the inequality is:
[tex]\[ x > -1.25 \][/tex]
So, the steps to solve the inequality [tex]\( 0.2(x + 20) - 3 > -7 - 6.2x \)[/tex] are:
1. Use the distributive property:
[tex]\[ 0.2x + 4 - 3 > -7 - 6.2x \][/tex]
[tex]\[ 0.2x + 1 > -7 - 6.2x \][/tex]
2. Combine like terms:
[tex]\[ 6.4x + 1 > -7 \][/tex]
3. Use the subtraction property of inequality:
[tex]\[ 6.4x > -8 \][/tex]
4. Use the division property of inequality:
[tex]\[ x > -1.25 \][/tex]
