Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+10}& = & -10 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10+6x } & = & -10 \color{red}{ -6x }\color{blue}{-10+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -10 \color{blue}{-10} \\\Leftrightarrow &19x & = &-20\\\Leftrightarrow & \color{red}{19}x & = &-20\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-20}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{19} } & & \\ & V = \left\{ \frac{-20}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1-x } & = & -10 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -10 \color{blue}{+1} \\\Leftrightarrow &5x & = &-9\\\Leftrightarrow & \color{red}{5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-6}& = & 12 \color{red}{ -3x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6+3x } & = & 12 \color{red}{ -3x }\color{blue}{+6+3x } \\\Leftrightarrow & -x \color{blue}{+3x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &2x & = &18\\\Leftrightarrow & \color{red}{2}x & = &18\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{18}{2} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+5}& = & -9 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5-10x } & = & -9 \color{red}{ +10x }\color{blue}{-5-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &-7x & = &-14\\\Leftrightarrow & \color{red}{-7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-14}{-7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-x } & = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &-15x & = &14\\\Leftrightarrow & \color{red}{-15}x & = &14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+6}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+6}\color{blue}{-6-x } & = & -14 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -14 \color{blue}{-6} \\\Leftrightarrow &-15x & = &-20\\\Leftrightarrow & \color{red}{-15}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+2}& = & -7 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2-10x } & = & -7 \color{red}{ +10x }\color{blue}{-2-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & -7 \color{blue}{-2} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+15}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15-9x } & = & 3 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & 3 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-14}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-14}\color{blue}{+14-x } & = & -14 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -14 \color{blue}{+14} \\\Leftrightarrow &-6x & = &0\\\Leftrightarrow & \color{red}{-6}x & = &0\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{0}{-6} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-7}& = & -9 \color{red}{ +10x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-10x } & = & -9 \color{red}{ +10x }\color{blue}{+7-10x } \\\Leftrightarrow & -13x \color{blue}{-10x } & = & -9 \color{blue}{+7} \\\Leftrightarrow &-23x & = &-2\\\Leftrightarrow & \color{red}{-23}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-2}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{2}{23} } & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+14}& = & 3 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14+14x } & = & 3 \color{red}{ -14x }\color{blue}{-14+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &19x & = &-11\\\Leftrightarrow & \color{red}{19}x & = &-11\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-11}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{19} } & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+1}& = & -11 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+1}\color{blue}{-1-4x } & = & -11 \color{red}{ +4x }\color{blue}{-1-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -11 \color{blue}{-1} \\\Leftrightarrow &-7x & = &-12\\\Leftrightarrow & \color{red}{-7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)