Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+11}& = & -13 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{+11}\color{blue}{-11-12x } & = & -13 \color{red}{ +12x }\color{blue}{-11-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & -13 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-24\\\Leftrightarrow & \color{red}{-11}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-24}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{24}{11} } & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+8}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-x } & = & -9 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -9 \color{blue}{-8} \\\Leftrightarrow &-3x & = &-17\\\Leftrightarrow & \color{red}{-3}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+14}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-x } & = & 1 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 1 \color{blue}{-14} \\\Leftrightarrow &-10x & = &-13\\\Leftrightarrow & \color{red}{-10}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{13}{10} } & & \\ & V = \left\{ \frac{13}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8-x } & = & 10 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &-12x & = &18\\\Leftrightarrow & \color{red}{-12}x & = &18\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{18}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+14}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14-8x } & = & 11 \color{red}{ +8x }\color{blue}{-14-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & 11 \color{blue}{-14} \\\Leftrightarrow &7x & = &-3\\\Leftrightarrow & \color{red}{7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+12}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-11x } & = & 10 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-7}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7+13x } & = & 1 \color{red}{ -13x }\color{blue}{+7+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 1 \color{blue}{+7} \\\Leftrightarrow &21x & = &8\\\Leftrightarrow & \color{red}{21}x & = &8\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{8}{21} \\\Leftrightarrow & \color{green}{ x = \frac{8}{21} } & & \\ & V = \left\{ \frac{8}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+3}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3-x } & = & 1 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 1 \color{blue}{-3} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+2}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2-7x } & = & -6 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &-4x & = &-8\\\Leftrightarrow & \color{red}{-4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-8}{-4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+11}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11-7x } & = & 5 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 5 \color{blue}{-11} \\\Leftrightarrow &3x & = &-6\\\Leftrightarrow & \color{red}{3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-6}{3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-14}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-x } & = & 12 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 12 \color{blue}{+14} \\\Leftrightarrow &-8x & = &26\\\Leftrightarrow & \color{red}{-8}x & = &26\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{26}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{4} } & & \\ & V = \left\{ \frac{-13}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-9}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9+7x } & = & 2 \color{red}{ -7x }\color{blue}{+9+7x } \\\Leftrightarrow & x \color{blue}{+7x } & = & 2 \color{blue}{+9} \\\Leftrightarrow &8x & = &11\\\Leftrightarrow & \color{red}{8}x & = &11\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{11}{8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)