Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{2})& = & -9x+\frac{7}{3} \\\Leftrightarrow & 28x-\frac{21}{2}& = & -9x+\frac{7}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{168}{ \color{blue}{6} }x- \frac{63}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{14}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 168x \color{red}{-63} & = & \color{red}{-54x} +14 \\\Leftrightarrow & 168x \color{red}{-63} \color{blue}{+63} \color{blue}{+54x} & = & \color{red}{-54x} +14 \color{blue}{+54x} \color{blue}{+63} \\\Leftrightarrow & 168x+54x& = & 14+63 \\\Leftrightarrow & \color{red}{222} x& = & 77 \\\Leftrightarrow & x = \frac{77}{222} & & \\ & V = \left\{ \frac{77}{222} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{2}{5})& = & -9x+\frac{7}{6} \\\Leftrightarrow & -18x+\frac{12}{5}& = & -9x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-540}{ \color{blue}{30} }x+ \frac{72}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -540x \color{red}{+72} & = & \color{red}{-270x} +35 \\\Leftrightarrow & -540x \color{red}{+72} \color{blue}{-72} \color{blue}{+270x} & = & \color{red}{-270x} +35 \color{blue}{+270x} \color{blue}{-72} \\\Leftrightarrow & -540x+270x& = & 35-72 \\\Leftrightarrow & \color{red}{-270} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-270} & & \\\Leftrightarrow & x = \frac{37}{270} & & \\ & V = \left\{ \frac{37}{270} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{11})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 8x+\frac{8}{11}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{528}{ \color{blue}{66} }x+ \frac{48}{ \color{blue}{66} })& = & (\frac{-330}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 528x \color{red}{+48} & = & \color{red}{-330x} +55 \\\Leftrightarrow & 528x \color{red}{+48} \color{blue}{-48} \color{blue}{+330x} & = & \color{red}{-330x} +55 \color{blue}{+330x} \color{blue}{-48} \\\Leftrightarrow & 528x+330x& = & 55-48 \\\Leftrightarrow & \color{red}{858} x& = & 7 \\\Leftrightarrow & x = \frac{7}{858} & & \\ & V = \left\{ \frac{7}{858} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{9})& = & -3x+\frac{7}{4} \\\Leftrightarrow & -8x+\frac{8}{9}& = & -3x+\frac{7}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-288}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} })& = & (\frac{-108}{ \color{blue}{36} }x+ \frac{63}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -288x \color{red}{+32} & = & \color{red}{-108x} +63 \\\Leftrightarrow & -288x \color{red}{+32} \color{blue}{-32} \color{blue}{+108x} & = & \color{red}{-108x} +63 \color{blue}{+108x} \color{blue}{-32} \\\Leftrightarrow & -288x+108x& = & 63-32 \\\Leftrightarrow & \color{red}{-180} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-180} & & \\\Leftrightarrow & x = \frac{-31}{180} & & \\ & V = \left\{ \frac{-31}{180} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{4}{5})& = & 7x+\frac{10}{11} \\\Leftrightarrow & 30x+\frac{24}{5}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+264} & = & \color{red}{385x} +50 \\\Leftrightarrow & 1650x \color{red}{+264} \color{blue}{-264} \color{blue}{-385x} & = & \color{red}{385x} +50 \color{blue}{-385x} \color{blue}{-264} \\\Leftrightarrow & 1650x-385x& = & 50-264 \\\Leftrightarrow & \color{red}{1265} x& = & -214 \\\Leftrightarrow & x = \frac{-214}{1265} & & \\ & V = \left\{ \frac{-214}{1265} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{7})& = & -8x+\frac{5}{8} \\\Leftrightarrow & -15x-\frac{10}{7}& = & -8x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-840}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{-448}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -840x \color{red}{-80} & = & \color{red}{-448x} +35 \\\Leftrightarrow & -840x \color{red}{-80} \color{blue}{+80} \color{blue}{+448x} & = & \color{red}{-448x} +35 \color{blue}{+448x} \color{blue}{+80} \\\Leftrightarrow & -840x+448x& = & 35+80 \\\Leftrightarrow & \color{red}{-392} x& = & 115 \\\Leftrightarrow & x = \frac{115}{-392} & & \\\Leftrightarrow & x = \frac{-115}{392} & & \\ & V = \left\{ \frac{-115}{392} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{3})& = & -2x+\frac{4}{3} \\\Leftrightarrow & 35x-\frac{14}{3}& = & -2x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{-6}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{-14} & = & \color{red}{-6x} +4 \\\Leftrightarrow & 105x \color{red}{-14} \color{blue}{+14} \color{blue}{+6x} & = & \color{red}{-6x} +4 \color{blue}{+6x} \color{blue}{+14} \\\Leftrightarrow & 105x+6x& = & 4+14 \\\Leftrightarrow & \color{red}{111} x& = & 18 \\\Leftrightarrow & x = \frac{18}{111} & & \\\Leftrightarrow & x = \frac{6}{37} & & \\ & V = \left\{ \frac{6}{37} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{2}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -30x-\frac{12}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{-60} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -1650x \color{red}{-60} \color{blue}{+60} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+60} \\\Leftrightarrow & -1650x+385x& = & 66+60 \\\Leftrightarrow & \color{red}{-1265} x& = & 126 \\\Leftrightarrow & x = \frac{126}{-1265} & & \\\Leftrightarrow & x = \frac{-126}{1265} & & \\ & V = \left\{ \frac{-126}{1265} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{11})& = & -9x+\frac{2}{7} \\\Leftrightarrow & -4x+\frac{10}{11}& = & -9x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-308}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -308x \color{red}{+70} & = & \color{red}{-693x} +22 \\\Leftrightarrow & -308x \color{red}{+70} \color{blue}{-70} \color{blue}{+693x} & = & \color{red}{-693x} +22 \color{blue}{+693x} \color{blue}{-70} \\\Leftrightarrow & -308x+693x& = & 22-70 \\\Leftrightarrow & \color{red}{385} x& = & -48 \\\Leftrightarrow & x = \frac{-48}{385} & & \\ & V = \left\{ \frac{-48}{385} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{5})& = & 7x+\frac{2}{5} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{+12} & = & \color{red}{35x} +2 \\\Leftrightarrow & 150x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +2 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & 150x-35x& = & 2-12 \\\Leftrightarrow & \color{red}{115} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{115} & & \\\Leftrightarrow & x = \frac{-2}{23} & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{7})& = & 3x+\frac{4}{9} \\\Leftrightarrow & 16x+\frac{16}{7}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1008}{ \color{blue}{63} }x+ \frac{144}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1008x \color{red}{+144} & = & \color{red}{189x} +28 \\\Leftrightarrow & 1008x \color{red}{+144} \color{blue}{-144} \color{blue}{-189x} & = & \color{red}{189x} +28 \color{blue}{-189x} \color{blue}{-144} \\\Leftrightarrow & 1008x-189x& = & 28-144 \\\Leftrightarrow & \color{red}{819} x& = & -116 \\\Leftrightarrow & x = \frac{-116}{819} & & \\ & V = \left\{ \frac{-116}{819} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{3}{11})& = & -5x+\frac{5}{7} \\\Leftrightarrow & -24x+\frac{18}{11}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+126} & = & \color{red}{-385x} +55 \\\Leftrightarrow & -1848x \color{red}{+126} \color{blue}{-126} \color{blue}{+385x} & = & \color{red}{-385x} +55 \color{blue}{+385x} \color{blue}{-126} \\\Leftrightarrow & -1848x+385x& = & 55-126 \\\Leftrightarrow & \color{red}{-1463} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-1463} & & \\\Leftrightarrow & x = \frac{71}{1463} & & \\ & V = \left\{ \frac{71}{1463} \right\} & \\\end{align}\)