Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-9}& = & -4 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9+5x } & = & -4 \color{red}{ -5x }\color{blue}{+9+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & -4 \color{blue}{+9} \\\Leftrightarrow &6x & = &5\\\Leftrightarrow & \color{red}{6}x & = &5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+7}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-x } & = & -10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -10 \color{blue}{-7} \\\Leftrightarrow &-11x & = &-17\\\Leftrightarrow & \color{red}{-11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+13}& = & -8 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13+5x } & = & -8 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -8 \color{blue}{-13} \\\Leftrightarrow &11x & = &-21\\\Leftrightarrow & \color{red}{11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6-x } & = & 9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 9 \color{blue}{-6} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-2}\color{blue}{+2-x } & = & 12 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 12 \color{blue}{+2} \\\Leftrightarrow &-13x & = &14\\\Leftrightarrow & \color{red}{-13}x & = &14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-12}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-x } & = & 4 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 4 \color{blue}{+12} \\\Leftrightarrow &-14x & = &16\\\Leftrightarrow & \color{red}{-14}x & = &16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+15}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15-x } & = & 5 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-10\\\Leftrightarrow & \color{red}{-15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-9}& = & -10 \color{red}{ +14x } \\\Leftrightarrow & 3x \color{red}{-9}\color{blue}{+9-14x } & = & -10 \color{red}{ +14x }\color{blue}{+9-14x } \\\Leftrightarrow & 3x \color{blue}{-14x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+1}& = & -13 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-14x } & = & -13 \color{red}{ +14x }\color{blue}{-1-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -13 \color{blue}{-1} \\\Leftrightarrow &-23x & = &-14\\\Leftrightarrow & \color{red}{-23}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-14}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{14}{23} } & & \\ & V = \left\{ \frac{14}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-15}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15-9x } & = & 8 \color{red}{ +9x }\color{blue}{+15-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 8 \color{blue}{+15} \\\Leftrightarrow &-17x & = &23\\\Leftrightarrow & \color{red}{-17}x & = &23\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{23}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{17} } & & \\ & V = \left\{ \frac{-23}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-14}& = & -1 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14+15x } & = & -1 \color{red}{ -15x }\color{blue}{+14+15x } \\\Leftrightarrow & 13x \color{blue}{+15x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &28x & = &13\\\Leftrightarrow & \color{red}{28}x & = &13\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}} & = & \frac{13}{28} \\\Leftrightarrow & \color{green}{ x = \frac{13}{28} } & & \\ & V = \left\{ \frac{13}{28} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+12}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{+12}\color{blue}{-12-13x } & = & 11 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &-12x & = &-1\\\Leftrightarrow & \color{red}{-12}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)