Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+6}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-x } & = & -7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &-5x & = &-13\\\Leftrightarrow & \color{red}{-5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-4}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-x } & = & 3 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 3 \color{blue}{+4} \\\Leftrightarrow &-12x & = &7\\\Leftrightarrow & \color{red}{-12}x & = &7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{12} } & & \\ & V = \left\{ \frac{-7}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-14}& = & 3 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-14x } & = & 3 \color{red}{ +14x }\color{blue}{+14-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 3 \color{blue}{+14} \\\Leftrightarrow &-23x & = &17\\\Leftrightarrow & \color{red}{-23}x & = &17\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{17}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{23} } & & \\ & V = \left\{ \frac{-17}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-6}& = & 2 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-4x } & = & 2 \color{red}{ +4x }\color{blue}{+6-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 2 \color{blue}{+6} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-2}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-2}\color{blue}{+2-x } & = & 7 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &-10x & = &9\\\Leftrightarrow & \color{red}{-10}x & = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+8}& = & 5 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+8}\color{blue}{-8+2x } & = & 5 \color{red}{ -2x }\color{blue}{-8+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &17x & = &-3\\\Leftrightarrow & \color{red}{17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-10}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10-x } & = & 4 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 4 \color{blue}{+10} \\\Leftrightarrow &-10x & = &14\\\Leftrightarrow & \color{red}{-10}x & = &14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8-x } & = & -2 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &11x & = &6\\\Leftrightarrow & \color{red}{11}x & = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+15}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15-x } & = & 10 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 10 \color{blue}{-15} \\\Leftrightarrow &-3x & = &-5\\\Leftrightarrow & \color{red}{-3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-9}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9-x } & = & 4 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-15}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-13x } & = & 10 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &-18x & = &25\\\Leftrightarrow & \color{red}{-18}x & = &25\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{25}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{18} } & & \\ & V = \left\{ \frac{-25}{18} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+2}& = & 13 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2+5x } & = & 13 \color{red}{ -5x }\color{blue}{-2+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &11x & = &11\\\Leftrightarrow & \color{red}{11}x & = &11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{11}{11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)