Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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