2/3x + 4/3 = -10/3

solve each equation by first eliminating all fractions

The solution of -2/3X + 4/3 = -10/3 by first eliminating all fractions is 7.0006

Solution:

We have been given an equation as follows:

And we have been asked to solve each equation by first eliminating all fractions.

The only way to solve this equation is by converting each of its components into decimals since it is stated in the question that we should not solve it in fraction form.

To do so we will individually convert the fractions to decimals and then substitute them back into the equation.

The 1st fraction in decimal form is:

The 2nd fraction in decimal form is:

And the 3rd fraction in decimal form is:

So, now we substitute the decimals instead of the fractions in the given equation as follows:

Therefore, the value of x in decimal from is 7.0006

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.