Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x-4)& = & -13 \color{red}{-} (-2-5x) \\\Leftrightarrow & 16x-16& = &-13+2+5x \\\Leftrightarrow & 16x \color{red}{-16} & = &-11 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{-16} \color{blue}{+16} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+16} \\\Leftrightarrow & 16x-5x& = &-11+16 \\\Leftrightarrow & 11x& = &5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-2x+3)& = & -2 \color{red}{-} (7-3x) \\\Leftrightarrow & -4x+6& = &-2-7+3x \\\Leftrightarrow & -4x \color{red}{+6} & = &-9 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &-9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & -4x-3x& = &-9-6 \\\Leftrightarrow & -7x& = &-15 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-15}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (x+5)& = & -6 \color{red}{+} (15-4x) \\\Leftrightarrow & 5x+25& = &-6+15-4x \\\Leftrightarrow & 5x \color{red}{+25} & = &9 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{+25} \color{blue}{-25} \color{blue}{+4x} & = &9 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-25} \\\Leftrightarrow & 5x+4x& = &9-25 \\\Leftrightarrow & 9x& = &-16 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-16}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-16}{9} & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-2x-5)& = & 13 \color{red}{+} (11+x) \\\Leftrightarrow & -4x-10& = &13+11+x \\\Leftrightarrow & -4x \color{red}{-10} & = &24 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -4x-x& = &24+10 \\\Leftrightarrow & -5x& = &34 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{34}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-34}{5} & & \\ & V = \left\{ \frac{-34}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-5x-1)& = & 10 \color{red}{+} (-2+3x) \\\Leftrightarrow & -25x-5& = &10-2+3x \\\Leftrightarrow & -25x \color{red}{-5} & = &8 \color{red}{+3x} \\\Leftrightarrow & -25x \color{red}{-5} \color{blue}{+5} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+5} \\\Leftrightarrow & -25x-3x& = &8+5 \\\Leftrightarrow & -28x& = &13 \\\Leftrightarrow & \frac{-28x}{ \color{red}{-28} }& = &\frac{13}{ \color{red}{-28} } \\\Leftrightarrow & x = \frac{-13}{28} & & \\ & V = \left\{ \frac{-13}{28} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (2x-1)& = & -8 \color{red}{-} (6+x) \\\Leftrightarrow & 4x-2& = &-8-6-x \\\Leftrightarrow & 4x \color{red}{-2} & = &-14 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 4x+x& = &-14+2 \\\Leftrightarrow & 5x& = &-12 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-12}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-12}{5} & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (x+4)& = & -4 \color{red}{+} (6-5x) \\\Leftrightarrow & 6x+24& = &-4+6-5x \\\Leftrightarrow & 6x \color{red}{+24} & = &2 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & 6x+5x& = &2-24 \\\Leftrightarrow & 11x& = &-22 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-22}{ \color{red}{11} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-6x-5)& = & 15 \color{red}{-} (10-5x) \\\Leftrightarrow & -36x-30& = &15-10+5x \\\Leftrightarrow & -36x \color{red}{-30} & = &5 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-30} \color{blue}{+30} \color{blue}{-5x} & = &5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+30} \\\Leftrightarrow & -36x-5x& = &5+30 \\\Leftrightarrow & -41x& = &35 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{35}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-35}{41} & & \\ & V = \left\{ \frac{-35}{41} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (2x+3)& = & -8 \color{red}{+} (-8+x) \\\Leftrightarrow & 8x+12& = &-8-8+x \\\Leftrightarrow & 8x \color{red}{+12} & = &-16 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 8x-x& = &-16-12 \\\Leftrightarrow & 7x& = &-28 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-28}{ \color{red}{7} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-5x+4)& = & -14 \color{red}{-} (2+x) \\\Leftrightarrow & -20x+16& = &-14-2-x \\\Leftrightarrow & -20x \color{red}{+16} & = &-16 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -20x+x& = &-16-16 \\\Leftrightarrow & -19x& = &-32 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-32}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{32}{19} & & \\ & V = \left\{ \frac{32}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-3x+6)& = & 9 \color{red}{+} (14-2x) \\\Leftrightarrow & -15x+30& = &9+14-2x \\\Leftrightarrow & -15x \color{red}{+30} & = &23 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+30} \color{blue}{-30} \color{blue}{+2x} & = &23 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-30} \\\Leftrightarrow & -15x+2x& = &23-30 \\\Leftrightarrow & -13x& = &-7 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-7}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-4x+3)& = & 10 \color{red}{-} (-13+3x) \\\Leftrightarrow & -20x+15& = &10+13-3x \\\Leftrightarrow & -20x \color{red}{+15} & = &23 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{+15} \color{blue}{-15} \color{blue}{+3x} & = &23 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-15} \\\Leftrightarrow & -20x+3x& = &23-15 \\\Leftrightarrow & -17x& = &8 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{8}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-8}{17} & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)