Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-3x-5)& = & -12 \color{red}{-} (-8+x) \\\Leftrightarrow & -18x-30& = &-12+8-x \\\Leftrightarrow & -18x \color{red}{-30} & = &-4 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -18x+x& = &-4+30 \\\Leftrightarrow & -17x& = &26 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{26}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-26}{17} & & \\ & V = \left\{ \frac{-26}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-4x-7)& = & 7 \color{red}{+} (-3+x) \\\Leftrightarrow & -20x-35& = &7-3+x \\\Leftrightarrow & -20x \color{red}{-35} & = &4 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & -20x-x& = &4+35 \\\Leftrightarrow & -21x& = &39 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{39}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-13}{7} & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-5x-1)& = & -2 \color{red}{-} (-8-3x) \\\Leftrightarrow & -10x-2& = &-2+8+3x \\\Leftrightarrow & -10x \color{red}{-2} & = &6 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-2} \color{blue}{+2} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+2} \\\Leftrightarrow & -10x-3x& = &6+2 \\\Leftrightarrow & -13x& = &8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (6x+4)& = & 15 \color{red}{-} (-14+x) \\\Leftrightarrow & 30x+20& = &15+14-x \\\Leftrightarrow & 30x \color{red}{+20} & = &29 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &29 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 30x+x& = &29-20 \\\Leftrightarrow & 31x& = &9 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{9}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{9}{31} & & \\ & V = \left\{ \frac{9}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (3x-3)& = & -3 \color{red}{-} (11+4x) \\\Leftrightarrow & 9x-9& = &-3-11-4x \\\Leftrightarrow & 9x \color{red}{-9} & = &-14 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{-9} \color{blue}{+9} \color{blue}{+4x} & = &-14 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+9} \\\Leftrightarrow & 9x+4x& = &-14+9 \\\Leftrightarrow & 13x& = &-5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x-1)& = & 3 \color{red}{-} (-2-5x) \\\Leftrightarrow & -3x-3& = &3+2+5x \\\Leftrightarrow & -3x \color{red}{-3} & = &5 \color{red}{+5x} \\\Leftrightarrow & -3x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & -3x-5x& = &5+3 \\\Leftrightarrow & -8x& = &8 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{8}{ \color{red}{-8} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x+5)& = & 8 \color{red}{-} (15+4x) \\\Leftrightarrow & -5x+25& = &8-15-4x \\\Leftrightarrow & -5x \color{red}{+25} & = &-7 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{+25} \color{blue}{-25} \color{blue}{+4x} & = &-7 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-25} \\\Leftrightarrow & -5x+4x& = &-7-25 \\\Leftrightarrow & -x& = &-32 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-32}{ \color{red}{-1} } \\\Leftrightarrow & x = 32 & & \\ & V = \left\{ 32 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-x+7)& = & -13 \color{red}{-} (8+4x) \\\Leftrightarrow & -3x+21& = &-13-8-4x \\\Leftrightarrow & -3x \color{red}{+21} & = &-21 \color{red}{-4x} \\\Leftrightarrow & -3x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &-21 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & -3x+4x& = &-21-21 \\\Leftrightarrow & x& = &-42 \\ & V = \left\{ -42 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (x-6)& = & -10 \color{red}{+} (-15-3x) \\\Leftrightarrow & 4x-24& = &-10-15-3x \\\Leftrightarrow & 4x \color{red}{-24} & = &-25 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &-25 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & 4x+3x& = &-25+24 \\\Leftrightarrow & 7x& = &-1 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-1}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-4x-5)& = & 9 \color{red}{-} (12+x) \\\Leftrightarrow & -16x-20& = &9-12-x \\\Leftrightarrow & -16x \color{red}{-20} & = &-3 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -16x+x& = &-3+20 \\\Leftrightarrow & -15x& = &17 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{17}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{-17}{15} & & \\ & V = \left\{ \frac{-17}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (x+5)& = & -9 \color{red}{+} (-14-3x) \\\Leftrightarrow & 4x+20& = &-9-14-3x \\\Leftrightarrow & 4x \color{red}{+20} & = &-23 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &-23 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & 4x+3x& = &-23-20 \\\Leftrightarrow & 7x& = &-43 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-43}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-43}{7} & & \\ & V = \left\{ \frac{-43}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (x+1)& = & -14 \color{red}{+} (15+3x) \\\Leftrightarrow & 2x+2& = &-14+15+3x \\\Leftrightarrow & 2x \color{red}{+2} & = &1 \color{red}{+3x} \\\Leftrightarrow & 2x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & 2x-3x& = &1-2 \\\Leftrightarrow & -x& = &-1 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-1}{ \color{red}{-1} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)