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3 years ago

-1 + 4x=3x +3 Solve for x ?

Mathematics

1 answer:

docker41 [41]3 years ago

5 0

Answer:

$x = 4$

Step-by-step explanation:

1. Regroup terms.

$4x - 1 = 3x + 3$

2. Add 1 to both sides.

$4x = 3x + 3 + 1$

3. Simplify 3x + 3 + 1 to 3x + 4.

$4x = 3x + 4$

4. Subtrect 3x from both sides.

$4x - 3x = 4$

5. Simplify 4x - 3x to x.

$x = 4$

Therefor, the answer is, x = 4.

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Answer:

$m\angle L = 100^{\circ}$ .

$m\angle J = 80^{\circ}$ .

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Step-by-step explanation:

Since segment $JM$ is parallel to segment $KL$ , quadrilateral $JKLM$ is a trapezoid.

Segment $JK$ and segment $LM$ (the two legs of this trapezoid) are equal in length. Hence, trapezoid $JKLM$ would be an isoscele trapezoid. By symmetry, $m\angle L = m \angle K = 100^{\circ}$ .

Line $JK$ traverses line $JM$ and line $KL$ . $\angle J$ and $\angle K$ are a pair of consecutive interior angles as they are both between $JM\!$ and $KL\!$ and are on the same side of the traversal, $JK\!$ .

Since line $JM$ is parallel to line $KL$ , any pair of consecutive interior angles between these two lines would add up to $180^{\circ}$ (supplementary angles.) Thus, $\angle J$ and $\angle K$ are supplementary angles; $m\angle J + m\angle K = 180^{\circ}$ .

Since $m\angle K = 100^{\circ}$ , $m\angle J = 180^{\circ} - m\angle K = 180^{\circ} - 100^{\circ} = 80^{\circ}$ .

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