Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-6}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-6}\color{blue}{+6-7x } & = & 4 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 4 \color{blue}{+6} \\\Leftrightarrow &8x & = &10\\\Leftrightarrow & \color{red}{8}x & = &10\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{10}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+6}& = & 5 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6+14x } & = & 5 \color{red}{ -14x }\color{blue}{-6+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &19x & = &-1\\\Leftrightarrow & \color{red}{19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+8}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8-x } & = & 13 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 13 \color{blue}{-8} \\\Leftrightarrow &7x & = &5\\\Leftrightarrow & \color{red}{7}x & = &5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-1}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1-13x } & = & -11 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & -11 \color{blue}{+1} \\\Leftrightarrow &-5x & = &-10\\\Leftrightarrow & \color{red}{-5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-10}{-5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+9}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9-x } & = & 10 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{-9} \\\Leftrightarrow &-15x & = &1\\\Leftrightarrow & \color{red}{-15}x & = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-7}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-7}\color{blue}{+7-7x } & = & 11 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 11 \color{blue}{+7} \\\Leftrightarrow &-5x & = &18\\\Leftrightarrow & \color{red}{-5}x & = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-10}& = & -8 \color{red}{ -6x } \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10+6x } & = & -8 \color{red}{ -6x }\color{blue}{+10+6x } \\\Leftrightarrow & -x \color{blue}{+6x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+11}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11-5x } & = & 9 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & 9 \color{blue}{-11} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-1}& = & 4 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1-4x } & = & 4 \color{red}{ +4x }\color{blue}{+1-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 4 \color{blue}{+1} \\\Leftrightarrow &-x & = &5\\\Leftrightarrow & \color{red}{-}x & = &5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{5}{-1} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+12}& = & -6 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12+15x } & = & -6 \color{red}{ -15x }\color{blue}{-12+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -6 \color{blue}{-12} \\\Leftrightarrow &19x & = &-18\\\Leftrightarrow & \color{red}{19}x & = &-18\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-18}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{19} } & & \\ & V = \left\{ \frac{-18}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+12}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12-9x } & = & 1 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & 1 \color{blue}{-12} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-10}& = & 3 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10+7x } & = & 3 \color{red}{ -7x }\color{blue}{+10+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 3 \color{blue}{+10} \\\Leftrightarrow &11x & = &13\\\Leftrightarrow & \color{red}{11}x & = &13\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{13}{11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)