Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+1}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1-13x } & = & 4 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & 4 \color{blue}{-1} \\\Leftrightarrow &-18x & = &3\\\Leftrightarrow & \color{red}{-18}x & = &3\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{3}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-12}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12-x } & = & 14 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 14 \color{blue}{+12} \\\Leftrightarrow &-11x & = &26\\\Leftrightarrow & \color{red}{-11}x & = &26\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{26}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{11} } & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-7}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-7}\color{blue}{+7+2x } & = & 2 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 2 \color{blue}{+7} \\\Leftrightarrow &17x & = &9\\\Leftrightarrow & \color{red}{17}x & = &9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-15}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-13x } & = & 7 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & 7 \color{blue}{+15} \\\Leftrightarrow &-2x & = &22\\\Leftrightarrow & \color{red}{-2}x & = &22\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{22}{-2} \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+10}& = & 7 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10-10x } & = & 7 \color{red}{ +10x }\color{blue}{-10-10x } \\\Leftrightarrow & 11x \color{blue}{-10x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+3}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3-11x } & = & 13 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &3x & = &10\\\Leftrightarrow & \color{red}{3}x & = &10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-1}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1-x } & = & -14 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -14 \color{blue}{+1} \\\Leftrightarrow &11x & = &-13\\\Leftrightarrow & \color{red}{11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-13}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+12}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+12}\color{blue}{-12-x } & = & 15 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 15 \color{blue}{-12} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+6}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6-x } & = & 15 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &10x & = &9\\\Leftrightarrow & \color{red}{10}x & = &9\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{9}{10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+8}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-x } & = & 15 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 15 \color{blue}{-8} \\\Leftrightarrow &-4x & = &7\\\Leftrightarrow & \color{red}{-4}x & = &7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+2}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-13x } & = & 1 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 1 \color{blue}{-2} \\\Leftrightarrow &-19x & = &-1\\\Leftrightarrow & \color{red}{-19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+1}& = & -9 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1+8x } & = & -9 \color{red}{ -8x }\color{blue}{-1+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &17x & = &-10\\\Leftrightarrow & \color{red}{17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)