Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-3x+7)& = & 9 \color{red}{-} (4-2x) \\\Leftrightarrow & -9x+21& = &9-4+2x \\\Leftrightarrow & -9x \color{red}{+21} & = &5 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{+21} \color{blue}{-21} \color{blue}{-2x} & = &5 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-21} \\\Leftrightarrow & -9x-2x& = &5-21 \\\Leftrightarrow & -11x& = &-16 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-16}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (6x+2)& = & 8 \color{red}{+} (15+x) \\\Leftrightarrow & 24x+8& = &8+15+x \\\Leftrightarrow & 24x \color{red}{+8} & = &23 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &23 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 24x-x& = &23-8 \\\Leftrightarrow & 23x& = &15 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{15}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{15}{23} & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (4x-7)& = & 10 \color{red}{-} (-15+x) \\\Leftrightarrow & 8x-14& = &10+15-x \\\Leftrightarrow & 8x \color{red}{-14} & = &25 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 8x+x& = &25+14 \\\Leftrightarrow & 9x& = &39 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{39}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{13}{3} & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-6x+6)& = & -11 \color{red}{-} (6+x) \\\Leftrightarrow & -30x+30& = &-11-6-x \\\Leftrightarrow & -30x \color{red}{+30} & = &-17 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -30x+x& = &-17-30 \\\Leftrightarrow & -29x& = &-47 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-47}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{47}{29} & & \\ & V = \left\{ \frac{47}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-5x-5)& = & 2 \color{red}{-} (10-3x) \\\Leftrightarrow & -10x-10& = &2-10+3x \\\Leftrightarrow & -10x \color{red}{-10} & = &-8 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -10x-3x& = &-8+10 \\\Leftrightarrow & -13x& = &2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-2x+6)& = & -10 \color{red}{-} (14+x) \\\Leftrightarrow & -8x+24& = &-10-14-x \\\Leftrightarrow & -8x \color{red}{+24} & = &-24 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -8x+x& = &-24-24 \\\Leftrightarrow & -7x& = &-48 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-48}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{48}{7} & & \\ & V = \left\{ \frac{48}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (5x+7)& = & -12 \color{red}{+} (2+x) \\\Leftrightarrow & 30x+42& = &-12+2+x \\\Leftrightarrow & 30x \color{red}{+42} & = &-10 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 30x-x& = &-10-42 \\\Leftrightarrow & 29x& = &-52 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-52}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-52}{29} & & \\ & V = \left\{ \frac{-52}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-x-4)& = & -3 \color{red}{-} (-5+x) \\\Leftrightarrow & -5x-20& = &-3+5-x \\\Leftrightarrow & -5x \color{red}{-20} & = &2 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -5x+x& = &2+20 \\\Leftrightarrow & -4x& = &22 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{22}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-11}{2} & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (x+1)& = & -8 \color{red}{+} (7+3x) \\\Leftrightarrow & 4x+4& = &-8+7+3x \\\Leftrightarrow & 4x \color{red}{+4} & = &-1 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & 4x-3x& = &-1-4 \\\Leftrightarrow & x& = &-5 \\ & V = \left\{ -5 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x+6)& = & -13 \color{red}{-} (-5+3x) \\\Leftrightarrow & 10x+30& = &-13+5-3x \\\Leftrightarrow & 10x \color{red}{+30} & = &-8 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+30} \color{blue}{-30} \color{blue}{+3x} & = &-8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-30} \\\Leftrightarrow & 10x+3x& = &-8-30 \\\Leftrightarrow & 13x& = &-38 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-38}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-38}{13} & & \\ & V = \left\{ \frac{-38}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (3x+3)& = & -7 \color{red}{+} (10+x) \\\Leftrightarrow & 12x+12& = &-7+10+x \\\Leftrightarrow & 12x \color{red}{+12} & = &3 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &3-12 \\\Leftrightarrow & 11x& = &-9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-9}{11} & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-4x-3)& = & 4 \color{red}{+} (-1+3x) \\\Leftrightarrow & -8x-6& = &4-1+3x \\\Leftrightarrow & -8x \color{red}{-6} & = &3 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{-6} \color{blue}{+6} \color{blue}{-3x} & = &3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+6} \\\Leftrightarrow & -8x-3x& = &3+6 \\\Leftrightarrow & -11x& = &9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-9}{11} & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)