Answered

IDNLearn.com: Your reliable source for finding expert answers. Whether your question is simple or complex, our community is here to provide detailed and trustworthy answers quickly and effectively.

Complete the steps to solve the inequality:

[tex]\[ 0.2(x+20) - 3 \ \textgreater \ -7 - 6.2x \][/tex]

1. Use the distributive property:
[tex]\[ 0.2x + 4 - 3 \ \textgreater \ -7 - 6.2x \][/tex]

2. Combine like terms:
[tex]\[ 0.2x + 1 \ \textgreater \ -7 - 6.2x \][/tex]

3. Use the addition property of inequality:
[tex]\[ 0.2x + 6.2x + 1 \ \textgreater \ -7 \][/tex]
[tex]\[ 6.4x + 1 \ \textgreater \ -7 \][/tex]

4. Use the subtraction property of inequality:
[tex]\[ 6.4x \ \textgreater \ -8 \][/tex]

5. Use the division property of inequality:
[tex]\[ x \ \textgreater \ -1.25 \][/tex]

Thus, the solution to the inequality is:
[tex]\[ x \ \textgreater \ -1.25 \][/tex]

Sagot :

GinnyAnsweridn
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]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Thank you for trusting IDNLearn.com with your questions. Visit us again for clear, concise, and accurate answers.