Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-6}& = & 14 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6+11x } & = & 14 \color{red}{ -11x }\color{blue}{+6+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 14 \color{blue}{+6} \\\Leftrightarrow &15x & = &20\\\Leftrightarrow & \color{red}{15}x & = &20\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{20}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10-x } & = & -9 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &-7x & = &-19\\\Leftrightarrow & \color{red}{-7}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{19}{7} } & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-5}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-x } & = & 5 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 5 \color{blue}{+5} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+15}& = & 8 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-14x } & = & 8 \color{red}{ +14x }\color{blue}{-15-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &-23x & = &-7\\\Leftrightarrow & \color{red}{-23}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-7}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{7}{23} } & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+8}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-x } & = & -10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -10 \color{blue}{-8} \\\Leftrightarrow &-9x & = &-18\\\Leftrightarrow & \color{red}{-9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-18}{-9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+11}& = & 15 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+11}\color{blue}{-11-12x } & = & 15 \color{red}{ +12x }\color{blue}{-11-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 15 \color{blue}{-11} \\\Leftrightarrow &-23x & = &4\\\Leftrightarrow & \color{red}{-23}x & = &4\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{4}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{23} } & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+2}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x } & = & -1 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -1 \color{blue}{-2} \\\Leftrightarrow &-4x & = &-3\\\Leftrightarrow & \color{red}{-4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+10}& = & 15 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10+3x } & = & 15 \color{red}{ -3x }\color{blue}{-10+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 15 \color{blue}{-10} \\\Leftrightarrow &7x & = &5\\\Leftrightarrow & \color{red}{7}x & = &5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-5}& = & -5 \color{red}{ +2x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5-2x } & = & -5 \color{red}{ +2x }\color{blue}{+5-2x } \\\Leftrightarrow & 5x \color{blue}{-2x } & = & -5 \color{blue}{+5} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+1}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-x } & = & -7 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -7 \color{blue}{-1} \\\Leftrightarrow &-5x & = &-8\\\Leftrightarrow & \color{red}{-5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-2}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2-x } & = & -14 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &-3x & = &-12\\\Leftrightarrow & \color{red}{-3}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-12}{-3} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-15}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15-x } & = & -13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -13 \color{blue}{+15} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)