Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+7}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-x } & = & 1 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &-10x & = &-6\\\Leftrightarrow & \color{red}{-10}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-6}\color{blue}{+6-x } & = & 6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &5x & = &12\\\Leftrightarrow & \color{red}{5}x & = &12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+2}& = & -1 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2-12x } & = & -1 \color{red}{ +12x }\color{blue}{-2-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & -1 \color{blue}{-2} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-12}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12-x } & = & 14 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 14 \color{blue}{+12} \\\Leftrightarrow &-11x & = &26\\\Leftrightarrow & \color{red}{-11}x & = &26\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{26}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{11} } & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+14}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14-5x } & = & -2 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & -2 \color{blue}{-14} \\\Leftrightarrow &-x & = &-16\\\Leftrightarrow & \color{red}{-}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-16}{-1} \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-4}& = & 9 \color{red}{ +2x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4-2x } & = & 9 \color{red}{ +2x }\color{blue}{+4-2x } \\\Leftrightarrow & 3x \color{blue}{-2x } & = & 9 \color{blue}{+4} \\\Leftrightarrow &x & = &13\\\Leftrightarrow & \color{red}{}x & = &13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 13 \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+15}& = & 1 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15+6x } & = & 1 \color{red}{ -6x }\color{blue}{-15+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 1 \color{blue}{-15} \\\Leftrightarrow &19x & = &-14\\\Leftrightarrow & \color{red}{19}x & = &-14\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-14}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{19} } & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+9}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9-7x } & = & 11 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & x \color{blue}{-7x } & = & 11 \color{blue}{-9} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-4}& = & 12 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4+12x } & = & 12 \color{red}{ -12x }\color{blue}{+4+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &25x & = &16\\\Leftrightarrow & \color{red}{25}x & = &16\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{16}{25} \\\Leftrightarrow & \color{green}{ x = \frac{16}{25} } & & \\ & V = \left\{ \frac{16}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-9}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-x } & = & -11 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -11 \color{blue}{+9} \\\Leftrightarrow &-11x & = &-2\\\Leftrightarrow & \color{red}{-11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+1}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-x } & = & 7 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 7 \color{blue}{-1} \\\Leftrightarrow &-12x & = &6\\\Leftrightarrow & \color{red}{-12}x & = &6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{+10}& = & -11 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10+5x } & = & -11 \color{red}{ -5x }\color{blue}{-10+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -11 \color{blue}{-10} \\\Leftrightarrow &8x & = &-21\\\Leftrightarrow & \color{red}{8}x & = &-21\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-21}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{8} } & & \\ & V = \left\{ \frac{-21}{8} \right\} & \\\end{align}\)