Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+4}& = & 13 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4-3x } & = & 13 \color{red}{ +3x }\color{blue}{-4-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &5x & = &9\\\Leftrightarrow & \color{red}{5}x & = &9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+5}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5-7x } & = & -7 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & -7 \color{blue}{-5} \\\Leftrightarrow &2x & = &-12\\\Leftrightarrow & \color{red}{2}x & = &-12\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-12}{2} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-2}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2-x } & = & -5 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &2x & = &-3\\\Leftrightarrow & \color{red}{2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+3}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-x } & = & 2 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-5}& = & 8 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5+4x } & = & 8 \color{red}{ -4x }\color{blue}{+5+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 8 \color{blue}{+5} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+15}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-7x } & = & -2 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & -2 \color{blue}{-15} \\\Leftrightarrow &-10x & = &-17\\\Leftrightarrow & \color{red}{-10}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{17}{10} } & & \\ & V = \left\{ \frac{17}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-x } & = & 10 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 10 \color{blue}{-6} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+10}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-x } & = & 2 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 2 \color{blue}{-10} \\\Leftrightarrow &-6x & = &-8\\\Leftrightarrow & \color{red}{-6}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+11}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11-13x } & = & 14 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &-17x & = &3\\\Leftrightarrow & \color{red}{-17}x & = &3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+13}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-11x } & = & -9 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -9 \color{blue}{-13} \\\Leftrightarrow &-16x & = &-22\\\Leftrightarrow & \color{red}{-16}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-22}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+14}& = & -3 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-9x } & = & -3 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &-17x & = &-17\\\Leftrightarrow & \color{red}{-17}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-17}{-17} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+7}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-x } & = & -10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -10 \color{blue}{-7} \\\Leftrightarrow &-15x & = &-17\\\Leftrightarrow & \color{red}{-15}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{17}{15} } & & \\ & V = \left\{ \frac{17}{15} \right\} & \\\end{align}\)