Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-3}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-3}\color{blue}{+3+11x } & = & 9 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & 9 \color{blue}{+3} \\\Leftrightarrow &14x & = &12\\\Leftrightarrow & \color{red}{14}x & = &12\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{12}{14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-15}& = & -10 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15-11x } & = & -10 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -10 \color{blue}{+15} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-6}& = & 7 \color{red}{ -14x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6+14x } & = & 7 \color{red}{ -14x }\color{blue}{+6+14x } \\\Leftrightarrow & -x \color{blue}{+14x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-13}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13-13x } & = & -8 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &-5x & = &5\\\Leftrightarrow & \color{red}{-5}x & = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2-x } & = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &11x & = &-5\\\Leftrightarrow & \color{red}{11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-6}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-6}\color{blue}{+6-x } & = & -15 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -15 \color{blue}{+6} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+14}& = & 10 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-4x } & = & 10 \color{red}{ +4x }\color{blue}{-14-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-4\\\Leftrightarrow & \color{red}{-11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+10}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-x } & = & -12 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -12 \color{blue}{-10} \\\Leftrightarrow &-4x & = &-22\\\Leftrightarrow & \color{red}{-4}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-22}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-3}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-7x } & = & 2 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &-17x & = &5\\\Leftrightarrow & \color{red}{-17}x & = &5\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{5}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{17} } & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+8}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-3x } & = & 15 \color{red}{ +3x }\color{blue}{-8-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & 15 \color{blue}{-8} \\\Leftrightarrow &-11x & = &7\\\Leftrightarrow & \color{red}{-11}x & = &7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+10}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10+7x } & = & -12 \color{red}{ -7x }\color{blue}{-10+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -12 \color{blue}{-10} \\\Leftrightarrow &12x & = &-22\\\Leftrightarrow & \color{red}{12}x & = &-22\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-22}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-9}& = & 2 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-9}\color{blue}{+9-8x } & = & 2 \color{red}{ +8x }\color{blue}{+9-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 2 \color{blue}{+9} \\\Leftrightarrow &-23x & = &11\\\Leftrightarrow & \color{red}{-23}x & = &11\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{11}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{23} } & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)