Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{-5}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5-8x } & = & 13 \color{red}{ +8x }\color{blue}{+5-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &-x & = &18\\\Leftrightarrow & \color{red}{-}x & = &18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{18}{-1} \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-15}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-x } & = & 9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 9 \color{blue}{+15} \\\Leftrightarrow &-14x & = &24\\\Leftrightarrow & \color{red}{-14}x & = &24\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{24}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+6}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6-7x } & = & 9 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & 9 \color{blue}{-6} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+13}& = & 15 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13-14x } & = & 15 \color{red}{ +14x }\color{blue}{-13-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-6}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-9x } & = & 5 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 5 \color{blue}{+6} \\\Leftrightarrow &-20x & = &11\\\Leftrightarrow & \color{red}{-20}x & = &11\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{11}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{20} } & & \\ & V = \left\{ \frac{-11}{20} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+14}& = & 12 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+14}\color{blue}{-14-6x } & = & 12 \color{red}{ +6x }\color{blue}{-14-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &-17x & = &-2\\\Leftrightarrow & \color{red}{-17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-1}& = & 10 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1+4x } & = & 10 \color{red}{ -4x }\color{blue}{+1+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 10 \color{blue}{+1} \\\Leftrightarrow &13x & = &11\\\Leftrightarrow & \color{red}{13}x & = &11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+4}& = & 12 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4-12x } & = & 12 \color{red}{ +12x }\color{blue}{-4-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+10}& = & 8 \color{red}{ -3x } \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10+3x } & = & 8 \color{red}{ -3x }\color{blue}{-10+3x } \\\Leftrightarrow & -x \color{blue}{+3x } & = & 8 \color{blue}{-10} \\\Leftrightarrow &2x & = &-2\\\Leftrightarrow & \color{red}{2}x & = &-2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-2}{2} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-12}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12-x } & = & 3 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &x & = &15\\\Leftrightarrow & \color{red}{}x & = &15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 15 \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-6}& = & 15 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-6}\color{blue}{+6+8x } & = & 15 \color{red}{ -8x }\color{blue}{+6+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &11x & = &21\\\Leftrightarrow & \color{red}{11}x & = &21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+4}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-7x } & = & -7 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)