Solved on Jan 22, 2024

Find the solution set for the inequality $7x > 43$ . Which answer choice correctly represents all values of $x$ that satisfy this inequality?

STEP 1

Assumptions
1. We are given the inequality $7x > 43$ .
2. We need to find the solution set for $x$ .
3. The solution set will include all values of $x$ that make the inequality true.

STEP 2

To find the solution set for the inequality, we need to isolate $x$ on one side of the inequality. We do this by dividing both sides of the inequality by 7.
$\frac{7x}{7} > \frac{43}{7}$

STEP 3

Simplify both sides of the inequality to solve for $x$ .
$x > \frac{43}{7}$

STEP 4

Calculate the value of the fraction on the right-hand side of the inequality.
$x > \frac{43}{7} = 6.142857...$

STEP 5

Since we are looking for all values of $x$ that satisfy the inequality, we can express the solution set as an interval.
$x > 6.142857...$

STEP 6

The solution set in interval notation is $(6.142857..., \infty)$ , which means that any value of $x$ greater than $6.142857...$ will make the inequality true.
The solution set is all values of $x$ such that $x > 6.142857...$ or, in decimal form, $x > 6.14$ (rounded to two decimal places).

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Find the solution set for the inequality $7x > 43$ . Which answer choice correctly represents all values of $x$ that satisfy this inequality?

STEP 1

Assumptions
1. We are given the inequality $7x > 43$ .
2. We need to find the solution set for $x$ .
3. The solution set will include all values of $x$ that make the inequality true.

STEP 2

To find the solution set for the inequality, we need to isolate $x$ on one side of the inequality. We do this by dividing both sides of the inequality by 7.
$\frac{7x}{7} > \frac{43}{7}$

STEP 3

Simplify both sides of the inequality to solve for $x$ .
$x > \frac{43}{7}$

STEP 4

Calculate the value of the fraction on the right-hand side of the inequality.
$x > \frac{43}{7} = 6.142857...$

STEP 5

Since we are looking for all values of $x$ that satisfy the inequality, we can express the solution set as an interval.
$x > 6.142857...$

STEP 6

The solution set in interval notation is $(6.142857..., \infty)$ , which means that any value of $x$ greater than $6.142857...$ will make the inequality true.
The solution set is all values of $x$ such that $x > 6.142857...$ or, in decimal form, $x > 6.14$ (rounded to two decimal places).

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Find the solution set for the inequality 7x>437x > 437x>43. Which answer choice correctly represents all values of xxx that satisfy this inequality?

STEP 1

Assumptions1. We are given the inequality 7x>437x > 437x>43.2. We need to find the solution set for xxx.3. The solution set will include all values of xxx that make the inequality true.

STEP 2

To find the solution set for the inequality, we need to isolate xxx on one side of the inequality. We do this by dividing both sides of the inequality by 7.7x7>437\frac{7x}{7} > \frac{43}{7}77x​>743​

STEP 3

Simplify both sides of the inequality to solve for xxx.x>437x > \frac{43}{7}x>743​

STEP 4

Calculate the value of the fraction on the right-hand side of the inequality.x>437=6.142857...x > \frac{43}{7} = 6.142857...x>743​=6.142857...

STEP 5

Since we are looking for all values of xxx that satisfy the inequality, we can express the solution set as an interval.x>6.142857...x > 6.142857...x>6.142857...

STEP 6

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Find the solution set for the inequality $7x > 43$ . Which answer choice correctly represents all values of $x$ that satisfy this inequality?

Assumptions
1. We are given the inequality $7x > 43$ .
2. We need to find the solution set for $x$ .
3. The solution set will include all values of $x$ that make the inequality true.

To find the solution set for the inequality, we need to isolate $x$ on one side of the inequality. We do this by dividing both sides of the inequality by 7.
$\frac{7x}{7} > \frac{43}{7}$

Simplify both sides of the inequality to solve for $x$ .
$x > \frac{43}{7}$

Calculate the value of the fraction on the right-hand side of the inequality.
$x > \frac{43}{7} = 6.142857...$

Since we are looking for all values of $x$ that satisfy the inequality, we can express the solution set as an interval.
$x > 6.142857...$