de la siguiente ecuación.
$\frac{3}{10} x+9=-\frac{3}{2} x-7$

Combine like terms by adding 2 3 ​ x to both sides and subtracting 9 from both sides: 10 3 ​ x + 2 3 ​ x = − 16 .
Find a common denominator and combine the x terms: 10 18 ​ x = − 16 .
Multiply both sides by the reciprocal of 10 18 ​ to isolate x: x = − 16 × 18 10 ​ .
Simplify the fraction to find the value of x: x = − 9 80 ​ ​ .

Explanation

Solving the equation Let's solve the equation step by step:

Original Equation: 10 3 ​ x + 9 = − 2 3 ​ x − 7

Add 2 3 ​ x to both sides: 10 3 ​ x + 2 3 ​ x + 9 = − 7

Subtract 9 from both sides: 10 3 ​ x + 2 3 ​ x = − 7 − 9

Simplify the right side: 10 3 ​ x + 2 3 ​ x = − 16

Find a common denominator for the x terms (which is 10): 10 3 ​ x + 10 15 ​ x = − 16

Combine the x terms: 10 18 ​ x = − 16

Multiply both sides by 18 10 ​ to solve for x: x = − 16 × 18 10 ​

Simplify the fraction: x = − 18 160 ​

Reduce the fraction by dividing both numerator and denominator by 2: x = − 9 80 ​


So, the solution to the equation is x = − 9 80 ​ .
Examples
Linear equations are used in everyday life to calculate costs, determine distances, and make predictions. For example, if you know the cost of each item you want to buy and have a budget, you can use a linear equation to determine how many items you can afford. Similarly, if you are traveling at a constant speed, you can use a linear equation to calculate how far you will travel in a certain amount of time.

Answered by GinnyAnswer | 2025-07-07