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"<" means "farther to the left on the number line " and ">" means "farther to the right on the number line". Multiplying by a negative number switches the sign, which is a reflection that turns left into right.

Double switch example:

1<2

multiply this by (-2):

-2>-4

multiply this by (-1):

2<4

Q: Why it is necessary to reverse the inequality symbol when multiplying both sides of an inequality by a negative number Provide an example to support your explanation?

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When multiplying or dividing a negative number or variable.

Think of a number line. The larger numbers are to the right and the smaller number to the left. For instance, five is less than seven. (5 < 7). When you multiply by a negative number, then the numbe with the larger absolute value is on the left, and the number with the smaller absolute value is to the right. (-5 > -7).

-7b < 49Remember, when dividing or multiplying by negative numbers, the sign of the inequality is flipped.Therefore:b > -7

positive and positive are positive positive and negative are negative negative and negative is positive

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Because your multiping the inverse to both sides

No. Only flip the inequality when multiplying or dividing by a negative number.

When multiplying or dividing a negative number or variable.

Only when what you're multiplying by/dividing by is negative.

You need to reverse the inequality symbol when multiplying both sides of an inequality by a negative number because you are changing the sign of both sides of the equation. Since inequality, such as "less than", means "to the left of" on the number line (where left is minus and right is plus) then a number that is less than another will be greater than the other if the signs were reversed. Example: 3 is less than 4, but -3 is greater than -4.

Think of a number line. The larger numbers are to the right and the smaller number to the left. For instance, five is less than seven. (5 < 7). When you multiply by a negative number, then the numbe with the larger absolute value is on the left, and the number with the smaller absolute value is to the right. (-5 > -7).

-7b < 49Remember, when dividing or multiplying by negative numbers, the sign of the inequality is flipped.Therefore:b > -7

positive and positive are positive positive and negative are negative negative and negative is positive

When an inequality is multiplied or divided by a negative number the inequality sign is reversed.Example : -x < 7 ......after multiplying by (say) -2 this becomes 2x > -14

Flip. You need to reverse the inequality when multiplying or dividing by a negative. -2x < 10 (-1)*(-2x) < (-1)*10 2x > -10 x > -5

When the two sides of the inequality are multiplied or divided by a negative number or term or expression.

It changes the direction of the inequality.