Solve 7/5x+1<6/5-3/4x

$$\frac { 7 } { 5 } x + 1 < \frac { 6 } { 5 } - \frac { 3 } { 4 } x$$

Solve for x

$$x<\frac{4}{43}$$

Solution Steps

Add \frac{3}{4}x to both sides.

$$\frac{7}{5}x+1+\frac{3}{4}x<\frac{6}{5}$$

Combine \frac{7}{5}x and \frac{3}{4}x to get \frac{43}{20}x.

$$\frac{43}{20}x+1<\frac{6}{5}$$

Subtract 1 from both sides.

$$\frac{43}{20}x<\frac{6}{5}-1$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{43}{20}x<\frac{6}{5}-\frac{5}{5}$$

Since \frac{6}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{43}{20}x<\frac{6-5}{5}$$

Subtract 5 from 6 to get 1.

$$\frac{43}{20}x<\frac{1}{5}$$

Multiply both sides by \frac{20}{43}, the reciprocal of \frac{43}{20}. Since \frac{43}{20} is positive, the inequality direction remains the same.

$$x<\frac{1}{5}\times \frac{20}{43}$$

Multiply \frac{1}{5} times \frac{20}{43} by multiplying numerator times numerator and denominator times denominator.

$$x<\frac{1\times 20}{5\times 43}$$

Do the multiplications in the fraction \frac{1\times 20}{5\times 43}.

$$x<\frac{20}{215}$$

Reduce the fraction \frac{20}{215} to lowest terms by extracting and canceling out 5.

$$x<\frac{4}{43}$$