| Step | Expression | Explanation |
|---|---|---|
| 1 | x – (x + (x – 1)) | Start with the original expression provided. |
| 2 | x – (x + x – 1) | Remove the innermost parentheses to simplify the expression within the outer parentheses. |
| 3 | x – x – x + 1 | Distribute the negative sign from the outer parentheses across each term inside it. This changes the signs of each term within the parentheses. |
| 4 | -x + 1 | Combine like terms: x – x – x equals -x for the terms involving ‘x’, and the constant term remains as +1. |
| Step | Expression | Explanation |
|---|---|---|
| 1 | 3x + 2(2x – 5) – 4(3x – 1) | Start with the original expression provided. |
| 2 | 3x + 4x – 10 – 12x + 4 | Distribute the constants into each set of parentheses: 2 * 2x = 4x, 2 * -5 = -10, -4 * 3x = -12x, and -4 * -1 = 4. |
| 3 | (3x + 4x – 12x) + (-10 + 4) | Group like terms together for easier simplification. Separate the terms involving ‘x’ from the constant terms. |
| 4 | -5x – 6 | Combine like terms: 3x + 4x – 12x = -5x for the terms involving ‘x’, and -10 + 4 = -6 for the constant terms. |
| Step | Expression | Explanation |
|---|---|---|
| 1 | 2(3x – 5) + 4(2x + 1) – 3(5x – 2) | Original expression |
| 2 | 6x – 10 + 8x + 4 – 15x + 6 | Distribute the constants: 2 * 3x – 2 * 5 + 4 * 2x + 4 * 1 – 3 * 5x – 3 * (-2) |
| 3 | (6x + 8x – 15x) + (-10 + 4 + 6) | Group like terms and simplify within parentheses |
| 4 | -1x + 0 | Combine like terms: 6x + 8x – 15x = -1x and -10 + 4 + 6 = 0 |
| 5 | -1x | Simplify the expression: -1x + 0 = -1x |
| Step | Expression | Explanation |
|---|---|---|
| 1 | 2x – (3x + 2(4 – x) – 2) + 3 | Start with the original expression |
| 2 | 2x – (3x + 8 – 2x – 2) + 3 | Distribute the constant 2 into the parentheses: 2 * 4 – 2 * x = 8 – 2x |
| 3 | 2x – (3x + 6) + 3 | Combine 8 and -2 within the parentheses: 8 – 2 = 6 |
| 4 | 2x – 3x – 6 + 3 | Remove the parentheses and distribute -1: -3x + 6 = -3x – 6 |
| 5 | -1x – 3 | Combine like terms: 2x – 3x = -1x and -6 + 3 = -3 |
| Step | Expression | Explanation |
|---|---|---|
| 1 | x – 2[-x – 2(x – 1) + 1] + 3 | Start with the original expression provided. |
| 2 | x – 2[-x – 2x + 2 + 1] + 3 | Remove the innermost parentheses by distributing -2 into (x – 1) to get -2x + 2. |
| 3 | x – 2[-3x + 3] + 3 | Combine like terms within the brackets to simplify it to -3x + 3. |
| 4 | x + 6x – 6 + 3 | Distribute the -2 across each term inside the brackets to get 6x – 6. |
| 5 | 7x – 3 | Combine all like terms to simplify the expression to 7x – 3. |
| Step | Expression | Explanation |
|---|---|---|
| 1 | x – 3[2x – 1 – 2(x – 1) + 1] + 2[3x – 2(x + 1) + 2] | Start with the original expression provided. |
| 2 | x – 3[2x – 1 – 2x + 2 + 1] + 2[3x – 2x – 2 + 2] | Remove the innermost parentheses by distributing -2 into (x – 1) and (x + 1) to get -2x + 2 and -2x – 2. |
| 3 | x – 3[0 + 2] + 2[x + 0] | Combine like terms within each set of brackets to simplify them to 0 and x. |
| 4 | x – 3[2] + 2[x] | Simplify the terms within the brackets to 2 and x. |
| 5 | x – 6 + 2x | Distribute the -3 and 2 across each term inside the brackets to get -6 and 2x. |
| 6 | 3x – 6 | Combine all like terms to simplify the expression to 3x – 6. |
Simplifying the Expression Step-by-Step
Original Expression
a – 2 [ -a – 3 ( -a – 4 ( -a + 1 ) + 2 ) + 3 ] + 4
Step 1: Distribute the -4 inside the innermost parentheses
No change needed for the innermost parentheses -a + 1.
Expression remains: a – 2 [ -a – 3 ( -a – 4 ( -a + 1 ) + 2 ) + 3 ] + 4
Step 2: Combine terms inside the next set of parentheses
Combine -a with -4(-a) and 1 with 2 inside the parentheses.
New expression: a – 2 [ -a – 3 ( 3a – 2 ) + 3 ] + 4
Step 3: Distribute the -3 inside the next set of parentheses
Multiply each term inside the parentheses 3a – 2 by -3.
New expression: a – 2 [ -a – 9a + 6 + 3 ] + 4
Step 4: Combine like terms inside the square brackets
Combine -a with -9a and 6 with 3 inside the square brackets.
New expression: a – 2 [ -10a + 9 ] + 4
Step 5: Distribute the -2 inside the square brackets
Multiply each term inside the square brackets -10a + 9 by -2.
New expression: a + 20a – 18 + 4
Step 6: Combine all like terms
Combine a with 20a and -18 with 4.
Final expression: 21a – 14