Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+3}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-x } & = & 6 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 6 \color{blue}{-3} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-13}& = & 10 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13+7x } & = & 10 \color{red}{ -7x }\color{blue}{+13+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &19x & = &23\\\Leftrightarrow & \color{red}{19}x & = &23\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{23}{19} \\\Leftrightarrow & \color{green}{ x = \frac{23}{19} } & & \\ & V = \left\{ \frac{23}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-9}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9-x } & = & 5 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 5 \color{blue}{+9} \\\Leftrightarrow &11x & = &14\\\Leftrightarrow & \color{red}{11}x & = &14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{14}{11} } & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+15}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15-7x } & = & 10 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & 10 \color{blue}{-15} \\\Leftrightarrow &-x & = &-5\\\Leftrightarrow & \color{red}{-}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-5}{-1} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-7}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7+11x } & = & -7 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &17x & = &0\\\Leftrightarrow & \color{red}{17}x & = &0\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{0}{17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+8}& = & 15 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8+15x } & = & 15 \color{red}{ -15x }\color{blue}{-8+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 15 \color{blue}{-8} \\\Leftrightarrow &23x & = &7\\\Leftrightarrow & \color{red}{23}x & = &7\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{7}{23} \\\Leftrightarrow & \color{green}{ x = \frac{7}{23} } & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-6}& = & -7 \color{red}{ +11x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-11x } & = & -7 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & -13x \color{blue}{-11x } & = & -7 \color{blue}{+6} \\\Leftrightarrow &-24x & = &-1\\\Leftrightarrow & \color{red}{-24}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-24}x}{ \color{blue}{ -24}} & = & \frac{-1}{-24} \\\Leftrightarrow & \color{green}{ x = \frac{1}{24} } & & \\ & V = \left\{ \frac{1}{24} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-13}& = & 5 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-13}\color{blue}{+13+6x } & = & 5 \color{red}{ -6x }\color{blue}{+13+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 5 \color{blue}{+13} \\\Leftrightarrow &19x & = &18\\\Leftrightarrow & \color{red}{19}x & = &18\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{18}{19} \\\Leftrightarrow & \color{green}{ x = \frac{18}{19} } & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+10}& = & 8 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10+5x } & = & 8 \color{red}{ -5x }\color{blue}{-10+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 8 \color{blue}{-10} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-1}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1-11x } & = & 2 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+15}& = & 15 \color{red}{ +12x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-12x } & = & 15 \color{red}{ +12x }\color{blue}{-15-12x } \\\Leftrightarrow & -7x \color{blue}{-12x } & = & 15 \color{blue}{-15} \\\Leftrightarrow &-19x & = &0\\\Leftrightarrow & \color{red}{-19}x & = &0\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{0}{-19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+9}& = & 4 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9-8x } & = & 4 \color{red}{ +8x }\color{blue}{-9-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & 4 \color{blue}{-9} \\\Leftrightarrow &-13x & = &-5\\\Leftrightarrow & \color{red}{-13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)