Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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