Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-11}& = & 8 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-10x } & = & 8 \color{red}{ +10x }\color{blue}{+11-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 8 \color{blue}{+11} \\\Leftrightarrow &-19x & = &19\\\Leftrightarrow & \color{red}{-19}x & = &19\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{19}{-19} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-8}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-13x } & = & 14 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & 14 \color{blue}{+8} \\\Leftrightarrow &x & = &22\\\Leftrightarrow & \color{red}{}x & = &22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 22 \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-12}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12-x } & = & 1 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 1 \color{blue}{+12} \\\Leftrightarrow &-8x & = &13\\\Leftrightarrow & \color{red}{-8}x & = &13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-13}& = & 14 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-13}\color{blue}{+13+4x } & = & 14 \color{red}{ -4x }\color{blue}{+13+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 14 \color{blue}{+13} \\\Leftrightarrow &13x & = &27\\\Leftrightarrow & \color{red}{13}x & = &27\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{27}{13} \\\Leftrightarrow & \color{green}{ x = \frac{27}{13} } & & \\ & V = \left\{ \frac{27}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-5}& = & -13 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-5}\color{blue}{+5+5x } & = & -13 \color{red}{ -5x }\color{blue}{+5+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -13 \color{blue}{+5} \\\Leftrightarrow &8x & = &-8\\\Leftrightarrow & \color{red}{8}x & = &-8\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-8}{8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-9}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & 6 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &-6x & = &15\\\Leftrightarrow & \color{red}{-6}x & = &15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-3}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-x } & = & 12 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 12 \color{blue}{+3} \\\Leftrightarrow &-12x & = &15\\\Leftrightarrow & \color{red}{-12}x & = &15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+15}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15-7x } & = & 8 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+11}& = & 3 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11+2x } & = & 3 \color{red}{ -2x }\color{blue}{-11+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 3 \color{blue}{-11} \\\Leftrightarrow &17x & = &-8\\\Leftrightarrow & \color{red}{17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-8}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{17} } & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-15}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-5x } & = & -2 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &3x & = &13\\\Leftrightarrow & \color{red}{3}x & = &13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+4}& = & 13 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4+13x } & = & 13 \color{red}{ -13x }\color{blue}{-4+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &27x & = &9\\\Leftrightarrow & \color{red}{27}x & = &9\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{9}{27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+6}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+6}\color{blue}{-6-x } & = & -7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &-15x & = &-13\\\Leftrightarrow & \color{red}{-15}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)