Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+1}& = & 3 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1+13x } & = & 3 \color{red}{ -13x }\color{blue}{-1+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 3 \color{blue}{-1} \\\Leftrightarrow &24x & = &2\\\Leftrightarrow & \color{red}{24}x & = &2\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{2}{24} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+10}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+10}\color{blue}{-10-x } & = & 6 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 6 \color{blue}{-10} \\\Leftrightarrow &-8x & = &-4\\\Leftrightarrow & \color{red}{-8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-11}& = & -13 \color{red}{ +3x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11-3x } & = & -13 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & 11x \color{blue}{-3x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &8x & = &-2\\\Leftrightarrow & \color{red}{8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+14}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14-x } & = & 2 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &-16x & = &-12\\\Leftrightarrow & \color{red}{-16}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-13}& = & 9 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-13}\color{blue}{+13-8x } & = & 9 \color{red}{ +8x }\color{blue}{+13-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 9 \color{blue}{+13} \\\Leftrightarrow &-x & = &22\\\Leftrightarrow & \color{red}{-}x & = &22\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{22}{-1} \\\Leftrightarrow & \color{green}{ x = -22 } & & \\ & V = \left\{ -22 \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+5}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & 5 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{-5} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-1}& = & -10 \color{red}{ +14x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1-14x } & = & -10 \color{red}{ +14x }\color{blue}{+1-14x } \\\Leftrightarrow & 3x \color{blue}{-14x } & = & -10 \color{blue}{+1} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+14}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14-7x } & = & 10 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &3x & = &-4\\\Leftrightarrow & \color{red}{3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+9}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+9}\color{blue}{-9-13x } & = & 2 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+14}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14-7x } & = & 3 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &3x & = &-11\\\Leftrightarrow & \color{red}{3}x & = &-11\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-11}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+13}& = & 5 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13-8x } & = & 5 \color{red}{ +8x }\color{blue}{-13-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 5 \color{blue}{-13} \\\Leftrightarrow &-23x & = &-8\\\Leftrightarrow & \color{red}{-23}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-8}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{8}{23} } & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-3}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-x } & = & 1 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 1 \color{blue}{+3} \\\Leftrightarrow &11x & = &4\\\Leftrightarrow & \color{red}{11}x & = &4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)