Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-10}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-10}\color{blue}{+10-x } & = & -4 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -4 \color{blue}{+10} \\\Leftrightarrow &2x & = &6\\\Leftrightarrow & \color{red}{2}x & = &6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{6}{2} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+15}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15-x } & = & -4 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -4 \color{blue}{-15} \\\Leftrightarrow &8x & = &-19\\\Leftrightarrow & \color{red}{8}x & = &-19\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-19}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{8} } & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-1}& = & -2 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1+5x } & = & -2 \color{red}{ -5x }\color{blue}{+1+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -2 \color{blue}{+1} \\\Leftrightarrow &8x & = &-1\\\Leftrightarrow & \color{red}{8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+1}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+1}\color{blue}{-1-x } & = & 6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &-4x & = &5\\\Leftrightarrow & \color{red}{-4}x & = &5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-8}& = & 12 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8+3x } & = & 12 \color{red}{ -3x }\color{blue}{+8+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &7x & = &20\\\Leftrightarrow & \color{red}{7}x & = &20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{20}{7} } & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-14}& = & 6 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14-4x } & = & 6 \color{red}{ +4x }\color{blue}{+14-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &11x & = &20\\\Leftrightarrow & \color{red}{11}x & = &20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-14}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x } & = & 9 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 9 \color{blue}{+14} \\\Leftrightarrow &-9x & = &23\\\Leftrightarrow & \color{red}{-9}x & = &23\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{23}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{9} } & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+9}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-x } & = & -7 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -7 \color{blue}{-9} \\\Leftrightarrow &-12x & = &-16\\\Leftrightarrow & \color{red}{-12}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-8}& = & 7 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8-6x } & = & 7 \color{red}{ +6x }\color{blue}{+8-6x } \\\Leftrightarrow & 7x \color{blue}{-6x } & = & 7 \color{blue}{+8} \\\Leftrightarrow &x & = &15\\\Leftrightarrow & \color{red}{}x & = &15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 15 \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{-9}& = & 12 \color{red}{ -9x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9+9x } & = & 12 \color{red}{ -9x }\color{blue}{+9+9x } \\\Leftrightarrow & x \color{blue}{+9x } & = & 12 \color{blue}{+9} \\\Leftrightarrow &10x & = &21\\\Leftrightarrow & \color{red}{10}x & = &21\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{21}{10} \\\Leftrightarrow & \color{green}{ x = \frac{21}{10} } & & \\ & V = \left\{ \frac{21}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+5}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-x } & = & 4 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+13}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-x } & = & 6 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 6 \color{blue}{-13} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)