Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-3}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-x } & = & 13 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 13 \color{blue}{+3} \\\Leftrightarrow &-11x & = &16\\\Leftrightarrow & \color{red}{-11}x & = &16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+6}& = & -7 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6-8x } & = & -7 \color{red}{ +8x }\color{blue}{-6-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &7x & = &-13\\\Leftrightarrow & \color{red}{7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15-x } & = & -2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &-13x & = &13\\\Leftrightarrow & \color{red}{-13}x & = &13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{13}{-13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+4}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4+11x } & = & 2 \color{red}{ -11x }\color{blue}{-4+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 2 \color{blue}{-4} \\\Leftrightarrow &23x & = &-2\\\Leftrightarrow & \color{red}{23}x & = &-2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{23} } & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-1}& = & 1 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{-1}\color{blue}{+1-10x } & = & 1 \color{red}{ +10x }\color{blue}{+1-10x } \\\Leftrightarrow & 11x \color{blue}{-10x } & = & 1 \color{blue}{+1} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+14}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-3x } & = & 14 \color{red}{ +3x }\color{blue}{-14-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &-8x & = &0\\\Leftrightarrow & \color{red}{-8}x & = &0\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{0}{-8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+5}& = & -11 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5+7x } & = & -11 \color{red}{ -7x }\color{blue}{-5+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &15x & = &-16\\\Leftrightarrow & \color{red}{15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-16}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+1}& = & 6 \color{red}{ +8x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1-8x } & = & 6 \color{red}{ +8x }\color{blue}{-1-8x } \\\Leftrightarrow & 9x \color{blue}{-8x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+3}& = & -3 \color{red}{ +8x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3-8x } & = & -3 \color{red}{ +8x }\color{blue}{-3-8x } \\\Leftrightarrow & 9x \color{blue}{-8x } & = & -3 \color{blue}{-3} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+10}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10-3x } & = & 4 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 4 \color{blue}{-10} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-6}& = & 7 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6+7x } & = & 7 \color{red}{ -7x }\color{blue}{+6+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &11x & = &13\\\Leftrightarrow & \color{red}{11}x & = &13\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{13}{11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-13}& = & 14 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{-13}\color{blue}{+13-4x } & = & 14 \color{red}{ +4x }\color{blue}{+13-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & 14 \color{blue}{+13} \\\Leftrightarrow &9x & = &27\\\Leftrightarrow & \color{red}{9}x & = &27\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{27}{9} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)