Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+8}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8-9x } & = & 10 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & 13x \color{blue}{-9x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &4x & = &2\\\Leftrightarrow & \color{red}{4}x & = &2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1-x } & = & 5 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &7x & = &4\\\Leftrightarrow & \color{red}{7}x & = &4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-3}& = & -6 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3+13x } & = & -6 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -6 \color{blue}{+3} \\\Leftrightarrow &24x & = &-3\\\Leftrightarrow & \color{red}{24}x & = &-3\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-3}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+11}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11-3x } & = & -11 \color{red}{ +3x }\color{blue}{-11-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & -11 \color{blue}{-11} \\\Leftrightarrow &7x & = &-22\\\Leftrightarrow & \color{red}{7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+5}& = & 7 \color{red}{ +4x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-4x } & = & 7 \color{red}{ +4x }\color{blue}{-5-4x } \\\Leftrightarrow & -5x \color{blue}{-4x } & = & 7 \color{blue}{-5} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-1}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-13x } & = & 1 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -11x \color{blue}{-13x } & = & 1 \color{blue}{+1} \\\Leftrightarrow &-24x & = &2\\\Leftrightarrow & \color{red}{-24}x & = &2\\\Leftrightarrow & \frac{\color{red}{-24}x}{ \color{blue}{ -24}} & = & \frac{2}{-24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+3}& = & -11 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3+11x } & = & -11 \color{red}{ -11x }\color{blue}{-3+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -11 \color{blue}{-3} \\\Leftrightarrow &23x & = &-14\\\Leftrightarrow & \color{red}{23}x & = &-14\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-14}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{23} } & & \\ & V = \left\{ \frac{-14}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+9}& = & 10 \color{red}{ -11x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9+11x } & = & 10 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & -15x \color{blue}{+11x } & = & 10 \color{blue}{-9} \\\Leftrightarrow &-4x & = &1\\\Leftrightarrow & \color{red}{-4}x & = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-8}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8+13x } & = & -5 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & -14x \color{blue}{+13x } & = & -5 \color{blue}{+8} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-7}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-13x } & = & 13 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -10x \color{blue}{-13x } & = & 13 \color{blue}{+7} \\\Leftrightarrow &-23x & = &20\\\Leftrightarrow & \color{red}{-23}x & = &20\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{20}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{23} } & & \\ & V = \left\{ \frac{-20}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-9}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9-9x } & = & 1 \color{red}{ +9x }\color{blue}{+9-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 1 \color{blue}{+9} \\\Leftrightarrow &-x & = &10\\\Leftrightarrow & \color{red}{-}x & = &10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{10}{-1} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+1}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1-9x } & = & 6 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & x \color{blue}{-9x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &-8x & = &5\\\Leftrightarrow & \color{red}{-8}x & = &5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)