Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+10}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-x } & = & -6 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -6 \color{blue}{-10} \\\Leftrightarrow &-12x & = &-16\\\Leftrightarrow & \color{red}{-12}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-2}& = & 5 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2+9x } & = & 5 \color{red}{ -9x }\color{blue}{+2+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 5 \color{blue}{+2} \\\Leftrightarrow &19x & = &7\\\Leftrightarrow & \color{red}{19}x & = &7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-5}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5-13x } & = & -12 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -12 \color{blue}{+5} \\\Leftrightarrow &-28x & = &-7\\\Leftrightarrow & \color{red}{-28}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-7}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-6}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6-11x } & = & 14 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & x \color{blue}{-11x } & = & 14 \color{blue}{+6} \\\Leftrightarrow &-10x & = &20\\\Leftrightarrow & \color{red}{-10}x & = &20\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{20}{-10} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-5}& = & -10 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5-5x } & = & -10 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & -10 \color{blue}{+5} \\\Leftrightarrow &-6x & = &-5\\\Leftrightarrow & \color{red}{-6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-13}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13-x } & = & -4 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -4 \color{blue}{+13} \\\Leftrightarrow &-10x & = &9\\\Leftrightarrow & \color{red}{-10}x & = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-x } & = & 12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &-11x & = &23\\\Leftrightarrow & \color{red}{-11}x & = &23\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{23}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{11} } & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-2}& = & 4 \color{red}{ +14x } \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2-14x } & = & 4 \color{red}{ +14x }\color{blue}{+2-14x } \\\Leftrightarrow & 3x \color{blue}{-14x } & = & 4 \color{blue}{+2} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-14}& = & 1 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14+8x } & = & 1 \color{red}{ -8x }\color{blue}{+14+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 1 \color{blue}{+14} \\\Leftrightarrow &11x & = &15\\\Leftrightarrow & \color{red}{11}x & = &15\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{15}{11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+14}& = & 5 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14-12x } & = & 5 \color{red}{ +12x }\color{blue}{-14-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & 5 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-11}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-x } & = & -12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+9}& = & -14 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-8x } & = & -14 \color{red}{ +8x }\color{blue}{-9-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & -14 \color{blue}{-9} \\\Leftrightarrow &-21x & = &-23\\\Leftrightarrow & \color{red}{-21}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-23}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{23}{21} } & & \\ & V = \left\{ \frac{23}{21} \right\} & \\\end{align}\)