Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+6}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-x } & = & -9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &-10x & = &-15\\\Leftrightarrow & \color{red}{-10}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-15}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-x } & = & -11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+3}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3-3x } & = & 15 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & 15 \color{blue}{-3} \\\Leftrightarrow &11x & = &12\\\Leftrightarrow & \color{red}{11}x & = &12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-10}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-x } & = & 10 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 10 \color{blue}{+10} \\\Leftrightarrow &-9x & = &20\\\Leftrightarrow & \color{red}{-9}x & = &20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{9} } & & \\ & V = \left\{ \frac{-20}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-12}& = & -5 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+5x } & = & -5 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &8x & = &7\\\Leftrightarrow & \color{red}{8}x & = &7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+11}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11-x } & = & 1 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 1 \color{blue}{-11} \\\Leftrightarrow &-15x & = &-10\\\Leftrightarrow & \color{red}{-15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-4}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{-4}\color{blue}{+4-9x } & = & -10 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & -10 \color{blue}{+4} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+10}& = & 8 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10+14x } & = & 8 \color{red}{ -14x }\color{blue}{-10+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 8 \color{blue}{-10} \\\Leftrightarrow &29x & = &-2\\\Leftrightarrow & \color{red}{29}x & = &-2\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-2}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{29} } & & \\ & V = \left\{ \frac{-2}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-12x & = &0\\\Leftrightarrow & \color{red}{-12}x & = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-1}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-1}\color{blue}{+1-x } & = & -13 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -13 \color{blue}{+1} \\\Leftrightarrow &-8x & = &-12\\\Leftrightarrow & \color{red}{-8}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-x } & = & -10 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &13x & = &-12\\\Leftrightarrow & \color{red}{13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+7}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7-x } & = & 8 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 8 \color{blue}{-7} \\\Leftrightarrow &5x & = &1\\\Leftrightarrow & \color{red}{5}x & = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)