Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To solve the inequality [tex]\(7x - 35 < 2(x - 5)\)[/tex], we need to follow a step-by-step process:
Step 1: Distribute the term on the right side.
[tex]\[ 7x - 35 < 2(x - 5) \][/tex]
Distribute the 2 to both terms inside the parentheses:
[tex]\[ 7x - 35 < 2x - 10 \][/tex]
Step 2: Move all terms involving [tex]\(x\)[/tex] to one side of the inequality.
Subtract [tex]\(2x\)[/tex] from both sides to isolate [tex]\(x\)[/tex] on one side:
[tex]\[ 7x - 2x - 35 < -10 \][/tex]
Step 3: Simplify the terms.
Combine like terms:
[tex]\[ 5x - 35 < -10 \][/tex]
Step 4: Isolate the [tex]\(x\)[/tex]-term.
Add 35 to both sides of the inequality to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[ 5x - 35 + 35 < -10 + 35 \][/tex]
[tex]\[ 5x < 25 \][/tex]
Step 5: Solve for [tex]\(x\)[/tex].
Divide both sides by 5 to isolate [tex]\(x\)[/tex]:
[tex]\[ x < 5 \][/tex]
Therefore, the solution to the inequality [tex]\(7x - 35 < 2(x - 5)\)[/tex] is:
[tex]\[ x < 5 \][/tex]
Step 1: Distribute the term on the right side.
[tex]\[ 7x - 35 < 2(x - 5) \][/tex]
Distribute the 2 to both terms inside the parentheses:
[tex]\[ 7x - 35 < 2x - 10 \][/tex]
Step 2: Move all terms involving [tex]\(x\)[/tex] to one side of the inequality.
Subtract [tex]\(2x\)[/tex] from both sides to isolate [tex]\(x\)[/tex] on one side:
[tex]\[ 7x - 2x - 35 < -10 \][/tex]
Step 3: Simplify the terms.
Combine like terms:
[tex]\[ 5x - 35 < -10 \][/tex]
Step 4: Isolate the [tex]\(x\)[/tex]-term.
Add 35 to both sides of the inequality to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[ 5x - 35 + 35 < -10 + 35 \][/tex]
[tex]\[ 5x < 25 \][/tex]
Step 5: Solve for [tex]\(x\)[/tex].
Divide both sides by 5 to isolate [tex]\(x\)[/tex]:
[tex]\[ x < 5 \][/tex]
Therefore, the solution to the inequality [tex]\(7x - 35 < 2(x - 5)\)[/tex] is:
[tex]\[ x < 5 \][/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.