Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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