Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-15}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-x } & = & -4 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -4 \color{blue}{+15} \\\Leftrightarrow &-14x & = &11\\\Leftrightarrow & \color{red}{-14}x & = &11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-8}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x } & = & 15 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &-15x & = &23\\\Leftrightarrow & \color{red}{-15}x & = &23\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{23}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{15} } & & \\ & V = \left\{ \frac{-23}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-12}& = & 9 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12-14x } & = & 9 \color{red}{ +14x }\color{blue}{+12-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & 9 \color{blue}{+12} \\\Leftrightarrow &-3x & = &21\\\Leftrightarrow & \color{red}{-3}x & = &21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{21}{-3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x } & = & -15 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -15 \color{blue}{-1} \\\Leftrightarrow &-8x & = &-16\\\Leftrightarrow & \color{red}{-8}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-16}{-8} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+13}& = & -10 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13+6x } & = & -10 \color{red}{ -6x }\color{blue}{-13+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &19x & = &-23\\\Leftrightarrow & \color{red}{19}x & = &-23\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-23}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{19} } & & \\ & V = \left\{ \frac{-23}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-6}& = & 7 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6-2x } & = & 7 \color{red}{ +2x }\color{blue}{+6-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &-3x & = &13\\\Leftrightarrow & \color{red}{-3}x & = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+8}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-7x } & = & -14 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -14 \color{blue}{-8} \\\Leftrightarrow &-13x & = &-22\\\Leftrightarrow & \color{red}{-13}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-22}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-1}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-1}\color{blue}{+1-x } & = & 15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &3x & = &16\\\Leftrightarrow & \color{red}{3}x & = &16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+10}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+10}\color{blue}{-10-x } & = & -11 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -11 \color{blue}{-10} \\\Leftrightarrow &-9x & = &-21\\\Leftrightarrow & \color{red}{-9}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-11}& = & 11 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11+6x } & = & 11 \color{red}{ -6x }\color{blue}{+11+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 11 \color{blue}{+11} \\\Leftrightarrow &13x & = &22\\\Leftrightarrow & \color{red}{13}x & = &22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-9}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-9}\color{blue}{+9-7x } & = & 9 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 9 \color{blue}{+9} \\\Leftrightarrow &-5x & = &18\\\Leftrightarrow & \color{red}{-5}x & = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-3}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-13x } & = & -12 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -12 \color{blue}{+3} \\\Leftrightarrow &-25x & = &-9\\\Leftrightarrow & \color{red}{-25}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-9}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{9}{25} } & & \\ & V = \left\{ \frac{9}{25} \right\} & \\\end{align}\)