Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-10}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10-7x } & = & 8 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & 13x \color{blue}{-7x } & = & 8 \color{blue}{+10} \\\Leftrightarrow &6x & = &18\\\Leftrightarrow & \color{red}{6}x & = &18\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{18}{6} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+3}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3-11x } & = & 13 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &4x & = &10\\\Leftrightarrow & \color{red}{4}x & = &10\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{10}{4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+3}& = & -5 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-14x } & = & -5 \color{red}{ +14x }\color{blue}{-3-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -5 \color{blue}{-3} \\\Leftrightarrow &-27x & = &-8\\\Leftrightarrow & \color{red}{-27}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-8}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{8}{27} } & & \\ & V = \left\{ \frac{8}{27} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-3}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-3}\color{blue}{+3-5x } & = & 2 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &-7x & = &5\\\Leftrightarrow & \color{red}{-7}x & = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-x } & = & -11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10-x } & = & -13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &-11x & = &-23\\\Leftrightarrow & \color{red}{-11}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-23}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{23}{11} } & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-15}& = & 7 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-12x } & = & 7 \color{red}{ +12x }\color{blue}{+15-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & 7 \color{blue}{+15} \\\Leftrightarrow &-x & = &22\\\Leftrightarrow & \color{red}{-}x & = &22\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{22}{-1} \\\Leftrightarrow & \color{green}{ x = -22 } & & \\ & V = \left\{ -22 \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+14}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14-5x } & = & 7 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 7 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+10}& = & 11 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+10}\color{blue}{-10+7x } & = & 11 \color{red}{ -7x }\color{blue}{-10+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 11 \color{blue}{-10} \\\Leftrightarrow &15x & = &1\\\Leftrightarrow & \color{red}{15}x & = &1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+9}& = & -13 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+9}\color{blue}{-9-3x } & = & -13 \color{red}{ +3x }\color{blue}{-9-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-22\\\Leftrightarrow & \color{red}{-5}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-22}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-9}& = & 6 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-9}\color{blue}{+9+5x } & = & 6 \color{red}{ -5x }\color{blue}{+9+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &8x & = &15\\\Leftrightarrow & \color{red}{8}x & = &15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-4}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4-13x } & = & 1 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &-5x & = &5\\\Leftrightarrow & \color{red}{-5}x & = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)