Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+13}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13-13x } & = & 11 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &-28x & = &-2\\\Leftrightarrow & \color{red}{-28}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-2}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-x } & = & 7 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 7 \color{blue}{-13} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-8}& = & 4 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8+15x } & = & 4 \color{red}{ -15x }\color{blue}{+8+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &19x & = &12\\\Leftrightarrow & \color{red}{19}x & = &12\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{12}{19} \\\Leftrightarrow & \color{green}{ x = \frac{12}{19} } & & \\ & V = \left\{ \frac{12}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+4}& = & 3 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4-12x } & = & 3 \color{red}{ +12x }\color{blue}{-4-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & 3 \color{blue}{-4} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-15}& = & -5 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15+11x } & = & -5 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -5 \color{blue}{+15} \\\Leftrightarrow &17x & = &10\\\Leftrightarrow & \color{red}{17}x & = &10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+1}& = & 7 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1+15x } & = & 7 \color{red}{ -15x }\color{blue}{-1+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 7 \color{blue}{-1} \\\Leftrightarrow &23x & = &6\\\Leftrightarrow & \color{red}{23}x & = &6\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{6}{23} \\\Leftrightarrow & \color{green}{ x = \frac{6}{23} } & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+15}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15-x } & = & 4 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 4 \color{blue}{-15} \\\Leftrightarrow &-16x & = &-11\\\Leftrightarrow & \color{red}{-16}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{11}{16} } & & \\ & V = \left\{ \frac{11}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-12}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-13x } & = & -4 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &-25x & = &8\\\Leftrightarrow & \color{red}{-25}x & = &8\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{8}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{25} } & & \\ & V = \left\{ \frac{-8}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+1}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1-7x } & = & -7 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -7 \color{blue}{-1} \\\Leftrightarrow &-17x & = &-8\\\Leftrightarrow & \color{red}{-17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+7}& = & 9 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7+x } & = & 9 \color{red}{ -x }\color{blue}{-7+x } \\\Leftrightarrow & x \color{blue}{+x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &2x & = &2\\\Leftrightarrow & \color{red}{2}x & = &2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{2}{2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-3}& = & 8 \color{red}{ +2x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3-2x } & = & 8 \color{red}{ +2x }\color{blue}{+3-2x } \\\Leftrightarrow & 13x \color{blue}{-2x } & = & 8 \color{blue}{+3} \\\Leftrightarrow &11x & = &11\\\Leftrightarrow & \color{red}{11}x & = &11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{11}{11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-9}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9-5x } & = & -8 \color{red}{ +5x }\color{blue}{+9-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &6x & = &1\\\Leftrightarrow & \color{red}{6}x & = &1\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{1}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)