Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-12}& = & 11 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-6x } & = & 11 \color{red}{ +6x }\color{blue}{+12-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 11 \color{blue}{+12} \\\Leftrightarrow &-11x & = &23\\\Leftrightarrow & \color{red}{-11}x & = &23\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{23}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{11} } & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+12}& = & -9 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12+3x } & = & -9 \color{red}{ -3x }\color{blue}{-12+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &10x & = &-21\\\Leftrightarrow & \color{red}{10}x & = &-21\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-21}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{10} } & & \\ & V = \left\{ \frac{-21}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+12}& = & -9 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12-8x } & = & -9 \color{red}{ +8x }\color{blue}{-12-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &-23x & = &-21\\\Leftrightarrow & \color{red}{-23}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-21}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{21}{23} } & & \\ & V = \left\{ \frac{21}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-x } & = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &-11x & = &14\\\Leftrightarrow & \color{red}{-11}x & = &14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-3}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-3}\color{blue}{+3-9x } & = & -10 \color{red}{ +9x }\color{blue}{+3-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-3}& = & -15 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3+12x } & = & -15 \color{red}{ -12x }\color{blue}{+3+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -15 \color{blue}{+3} \\\Leftrightarrow &25x & = &-12\\\Leftrightarrow & \color{red}{25}x & = &-12\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-12}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{25} } & & \\ & V = \left\{ \frac{-12}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+5}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-7x } & = & 10 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 10 \color{blue}{-5} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+6}& = & 4 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6-2x } & = & 4 \color{red}{ +2x }\color{blue}{-6-2x } \\\Leftrightarrow & 7x \color{blue}{-2x } & = & 4 \color{blue}{-6} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-16x & = &0\\\Leftrightarrow & \color{red}{-16}x & = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-12}& = & 11 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12+6x } & = & 11 \color{red}{ -6x }\color{blue}{+12+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 11 \color{blue}{+12} \\\Leftrightarrow &13x & = &23\\\Leftrightarrow & \color{red}{13}x & = &23\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{23}{13} \\\Leftrightarrow & \color{green}{ x = \frac{23}{13} } & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-1}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-x } & = & 14 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 14 \color{blue}{+1} \\\Leftrightarrow &-11x & = &15\\\Leftrightarrow & \color{red}{-11}x & = &15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+15}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15-x } & = & 3 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 3 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-12\\\Leftrightarrow & \color{red}{-15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)