QuestionSolve the compound inequality $-17 < 2y - 3 \leq 3$ and express the solution in interval notation. Use decimal values.

Studdy Solution

STEP 1

Assumptions1. The compound inequality is $-17<y-3\leq3$ . We are asked to solve the inequality and express the answer in interval notation.
3. We will use decimal form for numerical values.

STEP 2

The given compound inequality can be broken down into two separate inequalities.
$-17<2y-$ and $2y-\leq$

STEP 3

Let's solve the first inequality. To isolate $y$ , we need to first add3 to both sides of the inequality.
$-17+3<2y-3+3$

STEP 4

implify the inequality.
$-14<2y$

STEP 5

Next, divide both sides of the inequality by2 to solve for $y$ .
$\frac{-14}{2}<\frac{2y}{2}$

STEP 6

implify to get the solution for the first inequality.
$-<y$

STEP 7

Now, let's solve the second inequality. To isolate $y$ , we need to first add3 to both sides of the inequality.
$2y-3+3\leq3+3$

STEP 8

implify the inequality.
$2y\leq6$

STEP 9

Next, divide both sides of the inequality by2 to solve for $y$ .
$\frac{2y}{2}\leq\frac{6}{2}$

STEP 10

implify to get the solution for the second inequality.
$y\leq3$

STEP 11

Now, we combine the solutions of the two inequalities to form the solution of the compound inequality.
$-7<y\leq3$

STEP 12

Express the solution in interval notation. The solution is all $y$ such that $y$ is greater than -7 and less than or equal to.
$(-7,]$

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QuestionSolve the compound inequality $-17 < 2y - 3 \leq 3$ and express the solution in interval notation. Use decimal values.

Studdy Solution

STEP 1

Assumptions1. The compound inequality is $-17<y-3\leq3$ . We are asked to solve the inequality and express the answer in interval notation.
3. We will use decimal form for numerical values.

STEP 2

The given compound inequality can be broken down into two separate inequalities.
$-17<2y-$ and $2y-\leq$

STEP 3

Let's solve the first inequality. To isolate $y$ , we need to first add3 to both sides of the inequality.
$-17+3<2y-3+3$

STEP 4

implify the inequality.
$-14<2y$

STEP 5

Next, divide both sides of the inequality by2 to solve for $y$ .
$\frac{-14}{2}<\frac{2y}{2}$

STEP 6

implify to get the solution for the first inequality.
$-<y$

STEP 7

Now, let's solve the second inequality. To isolate $y$ , we need to first add3 to both sides of the inequality.
$2y-3+3\leq3+3$

STEP 8

implify the inequality.
$2y\leq6$

STEP 9

Next, divide both sides of the inequality by2 to solve for $y$ .
$\frac{2y}{2}\leq\frac{6}{2}$

STEP 10

implify to get the solution for the second inequality.
$y\leq3$

STEP 11

Now, we combine the solutions of the two inequalities to form the solution of the compound inequality.
$-7<y\leq3$

STEP 12

Express the solution in interval notation. The solution is all $y$ such that $y$ is greater than -7 and less than or equal to.
$(-7,]$

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QuestionSolve the compound inequality −17<2y−3≤3-17 < 2y - 3 \leq 3−17<2y−3≤3 and express the solution in interval notation. Use decimal values.

Studdy Solution

STEP 1

Assumptions1. The compound inequality is −17<y−3≤3-17<y-3\leq3−17<y−3≤3 . We are asked to solve the inequality and express the answer in interval notation.3. We will use decimal form for numerical values.

STEP 2

The given compound inequality can be broken down into two separate inequalities.−17<2y−-17<2y-−17<2y−and2y−≤2y-\leq2y−≤

STEP 3

Let's solve the first inequality. To isolate yyy, we need to first add3 to both sides of the inequality.−17+3<2y−3+3-17+3<2y-3+3−17+3<2y−3+3

STEP 4

implify the inequality.−14<2y-14<2y−14<2y

STEP 5

Next, divide both sides of the inequality by2 to solve for yyy.−142<2y2\frac{-14}{2}<\frac{2y}{2}2−14​<22y​

STEP 6

implify to get the solution for the first inequality.−<y-<y−<y

STEP 7

Now, let's solve the second inequality. To isolate yyy, we need to first add3 to both sides of the inequality.2y−3+3≤3+32y-3+3\leq3+32y−3+3≤3+3

STEP 8

implify the inequality.2y≤62y\leq62y≤6

STEP 9

Next, divide both sides of the inequality by2 to solve for yyy.2y2≤62\frac{2y}{2}\leq\frac{6}{2}22y​≤26​

STEP 10

implify to get the solution for the second inequality.y≤3y\leq3y≤3

STEP 11

Now, we combine the solutions of the two inequalities to form the solution of the compound inequality.−7<y≤3-7<y\leq3−7<y≤3

STEP 12

Express the solution in interval notation. The solution is all yyy such that yyy is greater than -7 and less than or equal to.(−7,](-7,](−7,]

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QuestionSolve the compound inequality $-17 < 2y - 3 \leq 3$ and express the solution in interval notation. Use decimal values.

Assumptions1. The compound inequality is $-17<y-3\leq3$ . We are asked to solve the inequality and express the answer in interval notation.
3. We will use decimal form for numerical values.

The given compound inequality can be broken down into two separate inequalities.
$-17<2y-$ and $2y-\leq$

Let's solve the first inequality. To isolate $y$ , we need to first add3 to both sides of the inequality.
$-17+3<2y-3+3$

implify the inequality.
$-14<2y$

Next, divide both sides of the inequality by2 to solve for $y$ .
$\frac{-14}{2}<\frac{2y}{2}$

implify to get the solution for the first inequality.
$-<y$

Now, let's solve the second inequality. To isolate $y$ , we need to first add3 to both sides of the inequality.
$2y-3+3\leq3+3$

implify the inequality.
$2y\leq6$

Next, divide both sides of the inequality by2 to solve for $y$ .
$\frac{2y}{2}\leq\frac{6}{2}$

implify to get the solution for the second inequality.
$y\leq3$

Now, we combine the solutions of the two inequalities to form the solution of the compound inequality.
$-7<y\leq3$

Express the solution in interval notation. The solution is all $y$ such that $y$ is greater than -7 and less than or equal to.
$(-7,]$