Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(3x-3=-9-8x\)
2. \(x+14=-14+10x\)
3. \(4x+1=-4+3x\)
4. \(2x-15=15+x\)
5. \(6x-9=14+5x\)
6. \(-14x+15=13+x\)
7. \(-12x+10=8+5x\)
8. \(15x+12=-9-11x\)
9. \(12x-14=-4+x\)
10. \(-x+4=-3-3x\)
11. \(7x+3=-10+2x\)
12. \(-11x-9=-13+x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-3}& = & -9 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-3}\color{blue}{+3+8x } & = & -9 \color{red}{ -8x }\color{blue}{+3+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+14}& = & -14 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14-10x } & = & -14 \color{red}{ +10x }\color{blue}{-14-10x } \\\Leftrightarrow & x \color{blue}{-10x } & = & -14 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-28\\\Leftrightarrow & \color{red}{-9}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-28}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{28}{9} } & & \\ & V = \left\{ \frac{28}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+1}& = & -4 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1-3x } & = & -4 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & -4 \color{blue}{-1} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-15}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15-x } & = & 15 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &x & = &30\\\Leftrightarrow & \color{red}{}x & = &30\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 30 \\\Leftrightarrow & \color{green}{ x = 30 } & & \\ & V = \left\{ 30 \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-9}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-9}\color{blue}{+9-5x } & = & 14 \color{red}{ +5x }\color{blue}{+9-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 14 \color{blue}{+9} \\\Leftrightarrow &x & = &23\\\Leftrightarrow & \color{red}{}x & = &23\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 23 \\\Leftrightarrow & \color{green}{ x = 23 } & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+15}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15-x } & = & 13 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 13 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-2\\\Leftrightarrow & \color{red}{-15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+10}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10-5x } & = & 8 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 8 \color{blue}{-10} \\\Leftrightarrow &-17x & = &-2\\\Leftrightarrow & \color{red}{-17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+12}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+12}\color{blue}{-12+11x } & = & -9 \color{red}{ -11x }\color{blue}{-12+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &26x & = &-21\\\Leftrightarrow & \color{red}{26}x & = &-21\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-21}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{26} } & & \\ & V = \left\{ \frac{-21}{26} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-14}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14-x } & = & -4 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -4 \color{blue}{+14} \\\Leftrightarrow &11x & = &10\\\Leftrightarrow & \color{red}{11}x & = &10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+4}& = & -3 \color{red}{ -3x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4+3x } & = & -3 \color{red}{ -3x }\color{blue}{-4+3x } \\\Leftrightarrow & -x \color{blue}{+3x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &2x & = &-7\\\Leftrightarrow & \color{red}{2}x & = &-7\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-7}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{+3}& = & -10 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3-2x } & = & -10 \color{red}{ +2x }\color{blue}{-3-2x } \\\Leftrightarrow & 7x \color{blue}{-2x } & = & -10 \color{blue}{-3} \\\Leftrightarrow &5x & = &-13\\\Leftrightarrow & \color{red}{5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9-x } & = & -13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &-12x & = &-4\\\Leftrightarrow & \color{red}{-12}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)