Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+8}& = & 7 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-3x } & = & 7 \color{red}{ +3x }\color{blue}{-8-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & 7 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-10}& = & -11 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10+11x } & = & -11 \color{red}{ -11x }\color{blue}{+10+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -11 \color{blue}{+10} \\\Leftrightarrow &23x & = &-1\\\Leftrightarrow & \color{red}{23}x & = &-1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+15}& = & -15 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15-14x } & = & -15 \color{red}{ +14x }\color{blue}{-15-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & -15 \color{blue}{-15} \\\Leftrightarrow &x & = &-30\\\Leftrightarrow & \color{red}{}x & = &-30\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -30 \\\Leftrightarrow & \color{green}{ x = -30 } & & \\ & V = \left\{ -30 \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+6}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6-7x } & = & 7 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &-20x & = &1\\\Leftrightarrow & \color{red}{-20}x & = &1\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{1}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{20} } & & \\ & V = \left\{ \frac{-1}{20} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+13}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-x } & = & 1 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 1 \color{blue}{-13} \\\Leftrightarrow &-9x & = &-12\\\Leftrightarrow & \color{red}{-9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-4}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4-7x } & = & 4 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &5x & = &8\\\Leftrightarrow & \color{red}{5}x & = &8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+3}& = & 11 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3+7x } & = & 11 \color{red}{ -7x }\color{blue}{-3+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 11 \color{blue}{-3} \\\Leftrightarrow &22x & = &8\\\Leftrightarrow & \color{red}{22}x & = &8\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{8}{22} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+3}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3-8x } & = & 12 \color{red}{ +8x }\color{blue}{-3-8x } \\\Leftrightarrow & 11x \color{blue}{-8x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &3x & = &9\\\Leftrightarrow & \color{red}{3}x & = &9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{9}{3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+1}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-x } & = & -13 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -13 \color{blue}{-1} \\\Leftrightarrow &-13x & = &-14\\\Leftrightarrow & \color{red}{-13}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+14}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14-5x } & = & -7 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &7x & = &-21\\\Leftrightarrow & \color{red}{7}x & = &-21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-21}{7} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-7}& = & 3 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7+3x } & = & 3 \color{red}{ -3x }\color{blue}{+7+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 3 \color{blue}{+7} \\\Leftrightarrow &13x & = &10\\\Leftrightarrow & \color{red}{13}x & = &10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-5}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-x } & = & -14 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)