Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+13}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-x } & = & 2 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 2 \color{blue}{-13} \\\Leftrightarrow &-6x & = &-11\\\Leftrightarrow & \color{red}{-6}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-11}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{+1}& = & -15 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1+4x } & = & -15 \color{red}{ -4x }\color{blue}{-1+4x } \\\Leftrightarrow & 13x \color{blue}{+4x } & = & -15 \color{blue}{-1} \\\Leftrightarrow &17x & = &-16\\\Leftrightarrow & \color{red}{17}x & = &-16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-14}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14-7x } & = & 11 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 11 \color{blue}{+14} \\\Leftrightarrow &8x & = &25\\\Leftrightarrow & \color{red}{8}x & = &25\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{25}{8} \\\Leftrightarrow & \color{green}{ x = \frac{25}{8} } & & \\ & V = \left\{ \frac{25}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-3}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-3}\color{blue}{+3-x } & = & -13 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -13 \color{blue}{+3} \\\Leftrightarrow &-9x & = &-10\\\Leftrightarrow & \color{red}{-9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+6}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-x } & = & -10 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -10 \color{blue}{-6} \\\Leftrightarrow &-5x & = &-16\\\Leftrightarrow & \color{red}{-5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+15}& = & -2 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15-10x } & = & -2 \color{red}{ +10x }\color{blue}{-15-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & -2 \color{blue}{-15} \\\Leftrightarrow &-x & = &-17\\\Leftrightarrow & \color{red}{-}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-17}{-1} \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-6}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6-11x } & = & 1 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & 9x \color{blue}{-11x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &-2x & = &7\\\Leftrightarrow & \color{red}{-2}x & = &7\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{7}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-14}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14-x } & = & 8 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 8 \color{blue}{+14} \\\Leftrightarrow &11x & = &22\\\Leftrightarrow & \color{red}{11}x & = &22\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{22}{11} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-7}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-x } & = & -5 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -5 \color{blue}{+7} \\\Leftrightarrow &-16x & = &2\\\Leftrightarrow & \color{red}{-16}x & = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+11}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11-11x } & = & -13 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -13 \color{blue}{-11} \\\Leftrightarrow &4x & = &-24\\\Leftrightarrow & \color{red}{4}x & = &-24\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-24}{4} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+3}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+3}\color{blue}{-3-x } & = & 8 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 8 \color{blue}{-3} \\\Leftrightarrow &-16x & = &5\\\Leftrightarrow & \color{red}{-16}x & = &5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{16} } & & \\ & V = \left\{ \frac{-5}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+9}& = & -8 \color{red}{ -4x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9+4x } & = & -8 \color{red}{ -4x }\color{blue}{-9+4x } \\\Leftrightarrow & x \color{blue}{+4x } & = & -8 \color{blue}{-9} \\\Leftrightarrow &5x & = &-17\\\Leftrightarrow & \color{red}{5}x & = &-17\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-17}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{5} } & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)