Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-x } & = & 14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 14 \color{blue}{-7} \\\Leftrightarrow &-10x & = &7\\\Leftrightarrow & \color{red}{-10}x & = &7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-2}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2-9x } & = & 12 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 12 \color{blue}{+2} \\\Leftrightarrow &5x & = &14\\\Leftrightarrow & \color{red}{5}x & = &14\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{14}{5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-1}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & 7 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &-15x & = &8\\\Leftrightarrow & \color{red}{-15}x & = &8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-7}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7-7x } & = & -5 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -5 \color{blue}{+7} \\\Leftrightarrow &3x & = &2\\\Leftrightarrow & \color{red}{3}x & = &2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11-x } & = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &11x & = &14\\\Leftrightarrow & \color{red}{11}x & = &14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{14}{11} } & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-x } & = & -3 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &-5x & = &1\\\Leftrightarrow & \color{red}{-5}x & = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-11}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-x } & = & 14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 14 \color{blue}{+11} \\\Leftrightarrow &-12x & = &25\\\Leftrightarrow & \color{red}{-12}x & = &25\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{25}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{12} } & & \\ & V = \left\{ \frac{-25}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+12}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-x } & = & 11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+6}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6-x } & = & 12 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -x \color{blue}{-x } & = & 12 \color{blue}{-6} \\\Leftrightarrow &-2x & = &6\\\Leftrightarrow & \color{red}{-2}x & = &6\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{6}{-2} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-8}& = & -8 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8+2x } & = & -8 \color{red}{ -2x }\color{blue}{+8+2x } \\\Leftrightarrow & 7x \color{blue}{+2x } & = & -8 \color{blue}{+8} \\\Leftrightarrow &9x & = &0\\\Leftrightarrow & \color{red}{9}x & = &0\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{0}{9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-12}& = & -8 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12+3x } & = & -8 \color{red}{ -3x }\color{blue}{+12+3x } \\\Leftrightarrow & 13x \color{blue}{+3x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &16x & = &4\\\Leftrightarrow & \color{red}{16}x & = &4\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{4}{16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7-x } & = & 14 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &7x & = &21\\\Leftrightarrow & \color{red}{7}x & = &21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{21}{7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)