Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (2x+6)& = & 10 \color{red}{+} (-1-5x) \\\Leftrightarrow & 8x+24& = &10-1-5x \\\Leftrightarrow & 8x \color{red}{+24} & = &9 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &9 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & 8x+5x& = &9-24 \\\Leftrightarrow & 13x& = &-15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (3x-5)& = & 10 \color{red}{-} (-1-5x) \\\Leftrightarrow & 18x-30& = &10+1+5x \\\Leftrightarrow & 18x \color{red}{-30} & = &11 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-30} \color{blue}{+30} \color{blue}{-5x} & = &11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+30} \\\Leftrightarrow & 18x-5x& = &11+30 \\\Leftrightarrow & 13x& = &41 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{41}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{41}{13} & & \\ & V = \left\{ \frac{41}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (3x-3)& = & -13 \color{red}{-} (15+x) \\\Leftrightarrow & 9x-9& = &-13-15-x \\\Leftrightarrow & 9x \color{red}{-9} & = &-28 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-28 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 9x+x& = &-28+9 \\\Leftrightarrow & 10x& = &-19 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{-19}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{-19}{10} & & \\ & V = \left\{ \frac{-19}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (5x+3)& = & 14 \color{red}{+} (9+x) \\\Leftrightarrow & 20x+12& = &14+9+x \\\Leftrightarrow & 20x \color{red}{+12} & = &23 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &23 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 20x-x& = &23-12 \\\Leftrightarrow & 19x& = &11 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{11}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{11}{19} & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (5x+5)& = & 13 \color{red}{+} (-15-2x) \\\Leftrightarrow & 15x+15& = &13-15-2x \\\Leftrightarrow & 15x \color{red}{+15} & = &-2 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &-2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & 15x+2x& = &-2-15 \\\Leftrightarrow & 17x& = &-17 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-17}{ \color{red}{17} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-5x-2)& = & -15 \color{red}{-} (12+x) \\\Leftrightarrow & -30x-12& = &-15-12-x \\\Leftrightarrow & -30x \color{red}{-12} & = &-27 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-27 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -30x+x& = &-27+12 \\\Leftrightarrow & -29x& = &-15 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-15}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{15}{29} & & \\ & V = \left\{ \frac{15}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (4x-2)& = & 8 \color{red}{+} (-14+x) \\\Leftrightarrow & 20x-10& = &8-14+x \\\Leftrightarrow & 20x \color{red}{-10} & = &-6 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 20x-x& = &-6+10 \\\Leftrightarrow & 19x& = &4 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{4}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{4}{19} & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-5x-4)& = & 2 \color{red}{-} (2+x) \\\Leftrightarrow & -10x-8& = &2-2-x \\\Leftrightarrow & -10x \color{red}{-8} & = &0 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -10x+x& = &0+8 \\\Leftrightarrow & -9x& = &8 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{8}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-8}{9} & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (5x-5)& = & 13 \color{red}{+} (2-2x) \\\Leftrightarrow & 15x-15& = &13+2-2x \\\Leftrightarrow & 15x \color{red}{-15} & = &15 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &15 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & 15x+2x& = &15+15 \\\Leftrightarrow & 17x& = &30 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{30}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{30}{17} & & \\ & V = \left\{ \frac{30}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-4x-4)& = & 2 \color{red}{+} (9+x) \\\Leftrightarrow & -12x-12& = &2+9+x \\\Leftrightarrow & -12x \color{red}{-12} & = &11 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &11+12 \\\Leftrightarrow & -13x& = &23 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{23}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (2x+1)& = & 4 \color{red}{-} (7+x) \\\Leftrightarrow & 6x+3& = &4-7-x \\\Leftrightarrow & 6x \color{red}{+3} & = &-3 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 6x+x& = &-3-3 \\\Leftrightarrow & 7x& = &-6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-6x+2)& = & -2 \color{red}{+} (11+x) \\\Leftrightarrow & -24x+8& = &-2+11+x \\\Leftrightarrow & -24x \color{red}{+8} & = &9 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -24x-x& = &9-8 \\\Leftrightarrow & -25x& = &1 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{1}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-1}{25} & & \\ & V = \left\{ \frac{-1}{25} \right\} & \\\end{align}\)