Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-15}& = & -13 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-3x } & = & -13 \color{red}{ +3x }\color{blue}{+15-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -13 \color{blue}{+15} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+8}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8-x } & = & 7 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 7 \color{blue}{-8} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+13}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-x } & = & 12 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 12 \color{blue}{-13} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-5}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5+11x } & = & 3 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 3 \color{blue}{+5} \\\Leftrightarrow &23x & = &8\\\Leftrightarrow & \color{red}{23}x & = &8\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{8}{23} \\\Leftrightarrow & \color{green}{ x = \frac{8}{23} } & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+11}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-x } & = & 9 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 9 \color{blue}{-11} \\\Leftrightarrow &-14x & = &-2\\\Leftrightarrow & \color{red}{-14}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-7}& = & 3 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7-6x } & = & 3 \color{red}{ +6x }\color{blue}{+7-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & 3 \color{blue}{+7} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+1}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1-x } & = & -5 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -5 \color{blue}{-1} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-3}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3-x } & = & 4 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 4 \color{blue}{+3} \\\Leftrightarrow &5x & = &7\\\Leftrightarrow & \color{red}{5}x & = &7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+13}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-x } & = & -9 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -9 \color{blue}{-13} \\\Leftrightarrow &-9x & = &-22\\\Leftrightarrow & \color{red}{-9}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-22}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{22}{9} } & & \\ & V = \left\{ \frac{22}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+1}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1+7x } & = & -13 \color{red}{ -7x }\color{blue}{-1+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -13 \color{blue}{-1} \\\Leftrightarrow &15x & = &-14\\\Leftrightarrow & \color{red}{15}x & = &-14\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-14}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+15}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15-4x } & = & -8 \color{red}{ +4x }\color{blue}{-15-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &-19x & = &-23\\\Leftrightarrow & \color{red}{-19}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-23}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{23}{19} } & & \\ & V = \left\{ \frac{23}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+2}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-x } & = & 2 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 2 \color{blue}{-2} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)