Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-13}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13-13x } & = & 2 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 2 \color{blue}{+13} \\\Leftrightarrow &-28x & = &15\\\Leftrightarrow & \color{red}{-28}x & = &15\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{15}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{28} } & & \\ & V = \left\{ \frac{-15}{28} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+11}& = & -6 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11+13x } & = & -6 \color{red}{ -13x }\color{blue}{-11+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -6 \color{blue}{-11} \\\Leftrightarrow &23x & = &-17\\\Leftrightarrow & \color{red}{23}x & = &-17\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-17}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{23} } & & \\ & V = \left\{ \frac{-17}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x } & = & -11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-24\\\Leftrightarrow & \color{red}{-11}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-24}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{24}{11} } & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-13}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-x } & = & -13 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -13 \color{blue}{+13} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+4}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-x } & = & -2 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &-8x & = &-6\\\Leftrightarrow & \color{red}{-8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+9}& = & -15 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9+7x } & = & -15 \color{red}{ -7x }\color{blue}{-9+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &19x & = &-24\\\Leftrightarrow & \color{red}{19}x & = &-24\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-24}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{19} } & & \\ & V = \left\{ \frac{-24}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-x } & = & 10 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &-11x & = &23\\\Leftrightarrow & \color{red}{-11}x & = &23\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{23}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{11} } & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+8}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+8}\color{blue}{-8-x } & = & 1 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 1 \color{blue}{-8} \\\Leftrightarrow &-10x & = &-7\\\Leftrightarrow & \color{red}{-10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+11}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11-5x } & = & -9 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -9 \color{blue}{-11} \\\Leftrightarrow &7x & = &-20\\\Leftrightarrow & \color{red}{7}x & = &-20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{7} } & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-10}& = & -9 \color{red}{ +8x } \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10-8x } & = & -9 \color{red}{ +8x }\color{blue}{+10-8x } \\\Leftrightarrow & -x \color{blue}{-8x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &-9x & = &1\\\Leftrightarrow & \color{red}{-9}x & = &1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+8}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & 11 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 11 \color{blue}{-8} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+10}& = & -11 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-8x } & = & -11 \color{red}{ +8x }\color{blue}{-10-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -11 \color{blue}{-10} \\\Leftrightarrow &-23x & = &-21\\\Leftrightarrow & \color{red}{-23}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-21}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{21}{23} } & & \\ & V = \left\{ \frac{21}{23} \right\} & \\\end{align}\)