To solve the linear equation -7x-14-3x = 16, the initial step is to consolidate the terms containing the variable x. The expression on the left side contains two distinct terms with the variable: -7x and -3x. Combining these like terms results in -10x, simplifying the equation to -10x - 14 = 16.
Isolating the Variable Term
The next phase focuses on isolating the term with the variable by moving the constant component to the opposite side of the equality. This is achieved by adding 14 to both sides of the equation. The operation transforms the left side into -10x, while the right side becomes 30, establishing the intermediate equation -10x = 30.
Understanding the Arithmetic
It is essential to maintain balance in the equation by performing the exact same operation on both sides. By adding 14 to the right side, you calculate 16 plus 14, which equals 30. The negative coefficient of -10x indicates that the solution for x will be a negative number, as a negative multiplied by a positive yields a positive result.
Calculating the Final Value
To determine the value of x, you must divide the isolated number 30 by the coefficient -10. Dividing 30 by -10 results in -3. Therefore, the value of x that satisfies the original condition is -3. This means that when x is replaced with -3, the left side of the equation will equal the right side.
| Step | Operation | Result |
| Original | -7x - 14 - 3x = 16 | -10x - 14 = 16 |
| Add 14 | -10x = 16 + 14 | -10x = 30 |
| Divide by -10 | x = 30 / -10 | x = -3 |
Practical Verification
Verifying the solution is a critical step to ensure accuracy in the computation. Substitute -3 for every instance of x in the original expression. The calculation becomes -7(-3) - 14 - 3(-3), which simplifies to 21 - 14 + 9. This sums to 16, confirming that the derived solution is correct.
Handling Negative Coefficients
Many individuals encounter difficulty when dealing with multiple negative signs. A helpful strategy is to focus on the like terms first. Rewriting the expression as (-7x - 3x) - 14 makes it clearer how the negatives combine to form -10x. Mastery of this sign management is a fundamental skill in algebra.
Applying the Solution
Understanding how to solve equations like -7x-14-3x = 16 provides a foundation for more complex mathematical concepts. This skill is applicable in various fields such as physics, engineering, and economics. The logical process of balancing equations remains consistent regardless of the complexity of the variables involved.
