Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+5}& = & -9 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-4x } & = & -9 \color{red}{ +4x }\color{blue}{-5-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &-11x & = &-14\\\Leftrightarrow & \color{red}{-11}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{14}{11} } & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+2}& = & 10 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2-12x } & = & 10 \color{red}{ +12x }\color{blue}{-2-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & 10 \color{blue}{-2} \\\Leftrightarrow &-x & = &8\\\Leftrightarrow & \color{red}{-}x & = &8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{8}{-1} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+10}& = & -6 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10+4x } & = & -6 \color{red}{ -4x }\color{blue}{-10+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -6 \color{blue}{-10} \\\Leftrightarrow &9x & = &-16\\\Leftrightarrow & \color{red}{9}x & = &-16\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-16}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-15}& = & 9 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-12x } & = & 9 \color{red}{ +12x }\color{blue}{+15-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 9 \color{blue}{+15} \\\Leftrightarrow &-23x & = &24\\\Leftrightarrow & \color{red}{-23}x & = &24\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{24}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{23} } & & \\ & V = \left\{ \frac{-24}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-3}& = & 6 \color{red}{ -12x } \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3+12x } & = & 6 \color{red}{ -12x }\color{blue}{+3+12x } \\\Leftrightarrow & -x \color{blue}{+12x } & = & 6 \color{blue}{+3} \\\Leftrightarrow &11x & = &9\\\Leftrightarrow & \color{red}{11}x & = &9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+10}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10-x } & = & 14 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 14 \color{blue}{-10} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+10}& = & -4 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10-9x } & = & -4 \color{red}{ +9x }\color{blue}{-10-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & -4 \color{blue}{-10} \\\Leftrightarrow &x & = &-14\\\Leftrightarrow & \color{red}{}x & = &-14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -14 \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-10}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10-x } & = & 14 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 14 \color{blue}{+10} \\\Leftrightarrow &11x & = &24\\\Leftrightarrow & \color{red}{11}x & = &24\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{24}{11} \\\Leftrightarrow & \color{green}{ x = \frac{24}{11} } & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2-x } & = & 15 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &12x & = &13\\\Leftrightarrow & \color{red}{12}x & = &13\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{13}{12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-3}& = & 3 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3+6x } & = & 3 \color{red}{ -6x }\color{blue}{+3+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &19x & = &6\\\Leftrightarrow & \color{red}{19}x & = &6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-4}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4-11x } & = & -11 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -11 \color{blue}{+4} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-12}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12-x } & = & -3 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -3 \color{blue}{+12} \\\Leftrightarrow &-11x & = &9\\\Leftrightarrow & \color{red}{-11}x & = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)