Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-7}& = & 12 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7+3x } & = & 12 \color{red}{ -3x }\color{blue}{+7+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &13x & = &19\\\Leftrightarrow & \color{red}{13}x & = &19\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{19}{13} \\\Leftrightarrow & \color{green}{ x = \frac{19}{13} } & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+8}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8-7x } & = & -4 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & 5x \color{blue}{-7x } & = & -4 \color{blue}{-8} \\\Leftrightarrow &-2x & = &-12\\\Leftrightarrow & \color{red}{-2}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-12}{-2} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+14}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-7x } & = & 4 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-20x & = &-10\\\Leftrightarrow & \color{red}{-20}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-10}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+10}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-x } & = & -3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &-15x & = &-13\\\Leftrightarrow & \color{red}{-15}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-10}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-13x } & = & 13 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &-25x & = &23\\\Leftrightarrow & \color{red}{-25}x & = &23\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{23}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{25} } & & \\ & V = \left\{ \frac{-23}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-4}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4-11x } & = & 5 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-3}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-11x } & = & -5 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+1}& = & -5 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+1}\color{blue}{-1+5x } & = & -5 \color{red}{ -5x }\color{blue}{-1+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -5 \color{blue}{-1} \\\Leftrightarrow &8x & = &-6\\\Leftrightarrow & \color{red}{8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-6}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-15}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15-x } & = & -7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &11x & = &8\\\Leftrightarrow & \color{red}{11}x & = &8\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{8}{11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+8}& = & -15 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8-3x } & = & -15 \color{red}{ +3x }\color{blue}{-8-3x } \\\Leftrightarrow & 7x \color{blue}{-3x } & = & -15 \color{blue}{-8} \\\Leftrightarrow &4x & = &-23\\\Leftrightarrow & \color{red}{4}x & = &-23\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-23}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{4} } & & \\ & V = \left\{ \frac{-23}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+11}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-9x } & = & 7 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 7 \color{blue}{-11} \\\Leftrightarrow &-17x & = &-4\\\Leftrightarrow & \color{red}{-17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+11}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11-11x } & = & -8 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-6x & = &-19\\\Leftrightarrow & \color{red}{-6}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-19}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{19}{6} } & & \\ & V = \left\{ \frac{19}{6} \right\} & \\\end{align}\)