Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-6}\color{blue}{+6-x } & = & 9 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 9 \color{blue}{+6} \\\Leftrightarrow &-10x & = &15\\\Leftrightarrow & \color{red}{-10}x & = &15\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{15}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+4}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+4}\color{blue}{-4-x } & = & 12 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &9x & = &8\\\Leftrightarrow & \color{red}{9}x & = &8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+6}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6-7x } & = & -15 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & -15 \color{blue}{-6} \\\Leftrightarrow &-9x & = &-21\\\Leftrightarrow & \color{red}{-9}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+9}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x } & = & 15 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 15 \color{blue}{-9} \\\Leftrightarrow &-8x & = &6\\\Leftrightarrow & \color{red}{-8}x & = &6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-6}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x } & = & 1 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &-4x & = &7\\\Leftrightarrow & \color{red}{-4}x & = &7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+15}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-9x } & = & 13 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 13 \color{blue}{-15} \\\Leftrightarrow &-17x & = &-2\\\Leftrightarrow & \color{red}{-17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-x } & = & 13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &-6x & = &18\\\Leftrightarrow & \color{red}{-6}x & = &18\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{18}{-6} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-12}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12-5x } & = & 4 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 4 \color{blue}{+12} \\\Leftrightarrow &-3x & = &16\\\Leftrightarrow & \color{red}{-3}x & = &16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-5}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5-11x } & = & 1 \color{red}{ +11x }\color{blue}{+5-11x } \\\Leftrightarrow & 9x \color{blue}{-11x } & = & 1 \color{blue}{+5} \\\Leftrightarrow &-2x & = &6\\\Leftrightarrow & \color{red}{-2}x & = &6\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{6}{-2} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+1}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1-7x } & = & -13 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & -13 \color{blue}{-1} \\\Leftrightarrow &-9x & = &-14\\\Leftrightarrow & \color{red}{-9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{14}{9} } & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+3}& = & -13 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3+2x } & = & -13 \color{red}{ -2x }\color{blue}{-3+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -13 \color{blue}{-3} \\\Leftrightarrow &17x & = &-16\\\Leftrightarrow & \color{red}{17}x & = &-16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+1}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-x } & = & -11 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -11 \color{blue}{-1} \\\Leftrightarrow &-10x & = &-12\\\Leftrightarrow & \color{red}{-10}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-12}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)