Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+5}& = & -8 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-14x } & = & -8 \color{red}{ +14x }\color{blue}{-5-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &-25x & = &-13\\\Leftrightarrow & \color{red}{-25}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-13}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{13}{25} } & & \\ & V = \left\{ \frac{13}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-12}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12-x } & = & -9 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -9 \color{blue}{+12} \\\Leftrightarrow &11x & = &3\\\Leftrightarrow & \color{red}{11}x & = &3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-8}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-x } & = & 12 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &-8x & = &20\\\Leftrightarrow & \color{red}{-8}x & = &20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+4}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x } & = & 11 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 11 \color{blue}{-4} \\\Leftrightarrow &-15x & = &7\\\Leftrightarrow & \color{red}{-15}x & = &7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+1}& = & 14 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1+7x } & = & 14 \color{red}{ -7x }\color{blue}{-1+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 14 \color{blue}{-1} \\\Leftrightarrow &22x & = &13\\\Leftrightarrow & \color{red}{22}x & = &13\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{13}{22} \\\Leftrightarrow & \color{green}{ x = \frac{13}{22} } & & \\ & V = \left\{ \frac{13}{22} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+1}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1-x } & = & -4 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -4 \color{blue}{-1} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-7}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-7}\color{blue}{+7-x } & = & 6 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 6 \color{blue}{+7} \\\Leftrightarrow &x & = &13\\\Leftrightarrow & \color{red}{}x & = &13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 13 \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-10}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10-11x } & = & 9 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & 9 \color{blue}{+10} \\\Leftrightarrow &-7x & = &19\\\Leftrightarrow & \color{red}{-7}x & = &19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-15}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-7x } & = & -5 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -5 \color{blue}{+15} \\\Leftrightarrow &-20x & = &10\\\Leftrightarrow & \color{red}{-20}x & = &10\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{10}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+7}& = & 1 \color{red}{ +2x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7-2x } & = & 1 \color{red}{ +2x }\color{blue}{-7-2x } \\\Leftrightarrow & 13x \color{blue}{-2x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-7}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-x } & = & -2 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -2 \color{blue}{+7} \\\Leftrightarrow &-8x & = &5\\\Leftrightarrow & \color{red}{-8}x & = &5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+5}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5-11x } & = & 14 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &-6x & = &9\\\Leftrightarrow & \color{red}{-6}x & = &9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)