Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-6}& = & 7 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6+2x } & = & 7 \color{red}{ -2x }\color{blue}{+6+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &11x & = &13\\\Leftrightarrow & \color{red}{11}x & = &13\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{13}{11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+1}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1-7x } & = & -14 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -14 \color{blue}{-1} \\\Leftrightarrow &3x & = &-15\\\Leftrightarrow & \color{red}{3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-15}{3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-8}& = & 5 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8+7x } & = & 5 \color{red}{ -7x }\color{blue}{+8+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & 5 \color{blue}{+8} \\\Leftrightarrow &18x & = &13\\\Leftrightarrow & \color{red}{18}x & = &13\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{13}{18} \\\Leftrightarrow & \color{green}{ x = \frac{13}{18} } & & \\ & V = \left\{ \frac{13}{18} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+3}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+3}\color{blue}{-3-x } & = & 2 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+15}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15-13x } & = & 6 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 6 \color{blue}{-15} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-11}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11-9x } & = & -13 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+3}& = & 9 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3+3x } & = & 9 \color{red}{ -3x }\color{blue}{-3+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 9 \color{blue}{-3} \\\Leftrightarrow &13x & = &6\\\Leftrightarrow & \color{red}{13}x & = &6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-2}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-2}\color{blue}{+2-11x } & = & 7 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-11}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-11}\color{blue}{+11-x } & = & -5 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -5 \color{blue}{+11} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+11}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-13x } & = & -14 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &-19x & = &-25\\\Leftrightarrow & \color{red}{-19}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-25}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{25}{19} } & & \\ & V = \left\{ \frac{25}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & 2 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+13}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13-11x } & = & 10 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & 10 \color{blue}{-13} \\\Leftrightarrow &-6x & = &-3\\\Leftrightarrow & \color{red}{-6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)