Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+7}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-x } & = & -11 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &-11x & = &-18\\\Leftrightarrow & \color{red}{-11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+10}\color{blue}{-10-x } & = & 13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 13 \color{blue}{-10} \\\Leftrightarrow &-8x & = &3\\\Leftrightarrow & \color{red}{-8}x & = &3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-7}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7+13x } & = & 9 \color{red}{ -13x }\color{blue}{+7+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 9 \color{blue}{+7} \\\Leftrightarrow &21x & = &16\\\Leftrightarrow & \color{red}{21}x & = &16\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{16}{21} \\\Leftrightarrow & \color{green}{ x = \frac{16}{21} } & & \\ & V = \left\{ \frac{16}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-9}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9-13x } & = & 4 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &-3x & = &13\\\Leftrightarrow & \color{red}{-3}x & = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-13}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-13}\color{blue}{+13-x } & = & 1 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 1 \color{blue}{+13} \\\Leftrightarrow &-6x & = &14\\\Leftrightarrow & \color{red}{-6}x & = &14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+10}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10-x } & = & 5 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 5 \color{blue}{-10} \\\Leftrightarrow &12x & = &-5\\\Leftrightarrow & \color{red}{12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-5}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+7}& = & -7 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+7}\color{blue}{-7+10x } & = & -7 \color{red}{ -10x }\color{blue}{-7+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &17x & = &-14\\\Leftrightarrow & \color{red}{17}x & = &-14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+7}& = & -11 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7+11x } & = & -11 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &17x & = &-18\\\Leftrightarrow & \color{red}{17}x & = &-18\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-18}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{17} } & & \\ & V = \left\{ \frac{-18}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-9}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9-7x } & = & 2 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & 2 \color{blue}{+9} \\\Leftrightarrow &2x & = &11\\\Leftrightarrow & \color{red}{2}x & = &11\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{11}{2} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+15}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-x } & = & 4 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 4 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-11\\\Leftrightarrow & \color{red}{-13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-7}& = & 12 \color{red}{ -9x } \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7+9x } & = & 12 \color{red}{ -9x }\color{blue}{+7+9x } \\\Leftrightarrow & x \color{blue}{+9x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &10x & = &19\\\Leftrightarrow & \color{red}{10}x & = &19\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{19}{10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-3}& = & -6 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-6x } & = & -6 \color{red}{ +6x }\color{blue}{+3-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -6 \color{blue}{+3} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)