Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1-x } & = & -6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &7x & = &-7\\\Leftrightarrow & \color{red}{7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-7}{7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-8}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8-5x } & = & 3 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & 7x \color{blue}{-5x } & = & 3 \color{blue}{+8} \\\Leftrightarrow &2x & = &11\\\Leftrightarrow & \color{red}{2}x & = &11\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{11}{2} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+6}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6-5x } & = & 13 \color{red}{ +5x }\color{blue}{-6-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 13 \color{blue}{-6} \\\Leftrightarrow &7x & = &7\\\Leftrightarrow & \color{red}{7}x & = &7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{7}{7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-8}& = & -10 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8+15x } & = & -10 \color{red}{ -15x }\color{blue}{+8+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -10 \color{blue}{+8} \\\Leftrightarrow &19x & = &-2\\\Leftrightarrow & \color{red}{19}x & = &-2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+10}& = & -3 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10+12x } & = & -3 \color{red}{ -12x }\color{blue}{-10+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &17x & = &-13\\\Leftrightarrow & \color{red}{17}x & = &-13\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-13}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{17} } & & \\ & V = \left\{ \frac{-13}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-x } & = & -10 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -10 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-19\\\Leftrightarrow & \color{red}{-9}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{19}{9} } & & \\ & V = \left\{ \frac{19}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-12}& = & 13 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-14x } & = & 13 \color{red}{ +14x }\color{blue}{+12-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 13 \color{blue}{+12} \\\Leftrightarrow &-27x & = &25\\\Leftrightarrow & \color{red}{-27}x & = &25\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{25}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{27} } & & \\ & V = \left\{ \frac{-25}{27} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+15}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15-14x } & = & -1 \color{red}{ +14x }\color{blue}{-15-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &-27x & = &-16\\\Leftrightarrow & \color{red}{-27}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-16}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{16}{27} } & & \\ & V = \left\{ \frac{16}{27} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-5}& = & 10 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5+2x } & = & 10 \color{red}{ -2x }\color{blue}{+5+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 10 \color{blue}{+5} \\\Leftrightarrow &17x & = &15\\\Leftrightarrow & \color{red}{17}x & = &15\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{15}{17} \\\Leftrightarrow & \color{green}{ x = \frac{15}{17} } & & \\ & V = \left\{ \frac{15}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+3}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3-x } & = & 10 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 10 \color{blue}{-3} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{-7}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7-x } & = & -6 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -6 \color{blue}{+7} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-x } & = & 14 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &-8x & = &21\\\Leftrightarrow & \color{red}{-8}x & = &21\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{21}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{8} } & & \\ & V = \left\{ \frac{-21}{8} \right\} & \\\end{align}\)