Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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