Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+10}& = & 6 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10+2x } & = & 6 \color{red}{ -2x }\color{blue}{-10+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & 6 \color{blue}{-10} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-5}& = & -12 \color{red}{ -5x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5+5x } & = & -12 \color{red}{ -5x }\color{blue}{+5+5x } \\\Leftrightarrow & -x \color{blue}{+5x } & = & -12 \color{blue}{+5} \\\Leftrightarrow &4x & = &-7\\\Leftrightarrow & \color{red}{4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-7}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+13}& = & 7 \color{red}{ +8x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13-8x } & = & 7 \color{red}{ +8x }\color{blue}{-13-8x } \\\Leftrightarrow & 11x \color{blue}{-8x } & = & 7 \color{blue}{-13} \\\Leftrightarrow &3x & = &-6\\\Leftrightarrow & \color{red}{3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-6}{3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+11}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+11}\color{blue}{-11-x } & = & -3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -3 \color{blue}{-11} \\\Leftrightarrow &-12x & = &-14\\\Leftrightarrow & \color{red}{-12}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-5}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{-5}\color{blue}{+5-9x } & = & -1 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+10}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10-x } & = & 2 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -x \color{blue}{-x } & = & 2 \color{blue}{-10} \\\Leftrightarrow &-2x & = &-8\\\Leftrightarrow & \color{red}{-2}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-8}{-2} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-9}& = & -3 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-10x } & = & -3 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & -3 \color{blue}{+9} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-11}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11-x } & = & -3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -3 \color{blue}{+11} \\\Leftrightarrow &-8x & = &8\\\Leftrightarrow & \color{red}{-8}x & = &8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{8}{-8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+5}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-11x } & = & 14 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &-21x & = &9\\\Leftrightarrow & \color{red}{-21}x & = &9\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{9}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-8}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-9x } & = & 8 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &-17x & = &16\\\Leftrightarrow & \color{red}{-17}x & = &16\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{16}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11-x } & = & -14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-8}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8-13x } & = & 12 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &-9x & = &20\\\Leftrightarrow & \color{red}{-9}x & = &20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{9} } & & \\ & V = \left\{ \frac{-20}{9} \right\} & \\\end{align}\)