Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+15}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-x } & = & 4 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 4 \color{blue}{-15} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+9}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-x } & = & -2 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &-16x & = &-11\\\Leftrightarrow & \color{red}{-16}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{11}{16} } & & \\ & V = \left\{ \frac{11}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+4}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-x } & = & 12 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &-3x & = &8\\\Leftrightarrow & \color{red}{-3}x & = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-4}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & -2 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -2 \color{blue}{+4} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+1}& = & -7 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-6x } & = & -7 \color{red}{ +6x }\color{blue}{-1-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & -7 \color{blue}{-1} \\\Leftrightarrow &-17x & = &-8\\\Leftrightarrow & \color{red}{-17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-4}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4-x } & = & 15 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 15 \color{blue}{+4} \\\Leftrightarrow &11x & = &19\\\Leftrightarrow & \color{red}{11}x & = &19\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{19}{11} \\\Leftrightarrow & \color{green}{ x = \frac{19}{11} } & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-13}\color{blue}{+13-x } & = & 7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &-6x & = &20\\\Leftrightarrow & \color{red}{-6}x & = &20\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{20}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-8}& = & 1 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8+2x } & = & 1 \color{red}{ -2x }\color{blue}{+8+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &3x & = &9\\\Leftrightarrow & \color{red}{3}x & = &9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{9}{3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+4}& = & -10 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4-11x } & = & -10 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &3x & = &-14\\\Leftrightarrow & \color{red}{3}x & = &-14\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-14}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{3} } & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+2}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2-13x } & = & -14 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -14 \color{blue}{-2} \\\Leftrightarrow &-3x & = &-16\\\Leftrightarrow & \color{red}{-3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+11}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11-x } & = & -15 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -15 \color{blue}{-11} \\\Leftrightarrow &-15x & = &-26\\\Leftrightarrow & \color{red}{-15}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-26}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{26}{15} } & & \\ & V = \left\{ \frac{26}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+11}& = & -13 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11+6x } & = & -13 \color{red}{ -6x }\color{blue}{-11+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -13 \color{blue}{-11} \\\Leftrightarrow &19x & = &-24\\\Leftrightarrow & \color{red}{19}x & = &-24\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-24}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{19} } & & \\ & V = \left\{ \frac{-24}{19} \right\} & \\\end{align}\)