Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{3})& = & 2x+\frac{9}{4} \\\Leftrightarrow & 25x+\frac{10}{3}& = & 2x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{300}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} })& = & (\frac{24}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 300x \color{red}{+40} & = & \color{red}{24x} +27 \\\Leftrightarrow & 300x \color{red}{+40} \color{blue}{-40} \color{blue}{-24x} & = & \color{red}{24x} +27 \color{blue}{-24x} \color{blue}{-40} \\\Leftrightarrow & 300x-24x& = & 27-40 \\\Leftrightarrow & \color{red}{276} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{276} & & \\ & V = \left\{ \frac{-13}{276} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{6})& = & -3x+\frac{2}{7} \\\Leftrightarrow & -14x+\frac{35}{6}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-588}{ \color{blue}{42} }x+ \frac{245}{ \color{blue}{42} })& = & (\frac{-126}{ \color{blue}{42} }x+ \frac{12}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -588x \color{red}{+245} & = & \color{red}{-126x} +12 \\\Leftrightarrow & -588x \color{red}{+245} \color{blue}{-245} \color{blue}{+126x} & = & \color{red}{-126x} +12 \color{blue}{+126x} \color{blue}{-245} \\\Leftrightarrow & -588x+126x& = & 12-245 \\\Leftrightarrow & \color{red}{-462} x& = & -233 \\\Leftrightarrow & x = \frac{-233}{-462} & & \\\Leftrightarrow & x = \frac{233}{462} & & \\ & V = \left\{ \frac{233}{462} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{11})& = & -7x+\frac{5}{6} \\\Leftrightarrow & 4x-\frac{6}{11}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{264}{ \color{blue}{66} }x- \frac{36}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 264x \color{red}{-36} & = & \color{red}{-462x} +55 \\\Leftrightarrow & 264x \color{red}{-36} \color{blue}{+36} \color{blue}{+462x} & = & \color{red}{-462x} +55 \color{blue}{+462x} \color{blue}{+36} \\\Leftrightarrow & 264x+462x& = & 55+36 \\\Leftrightarrow & \color{red}{726} x& = & 91 \\\Leftrightarrow & x = \frac{91}{726} & & \\ & V = \left\{ \frac{91}{726} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{3})& = & -9x+\frac{3}{8} \\\Leftrightarrow & 14x+\frac{14}{3}& = & -9x+\frac{3}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{336}{ \color{blue}{24} }x+ \frac{112}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 336x \color{red}{+112} & = & \color{red}{-216x} +9 \\\Leftrightarrow & 336x \color{red}{+112} \color{blue}{-112} \color{blue}{+216x} & = & \color{red}{-216x} +9 \color{blue}{+216x} \color{blue}{-112} \\\Leftrightarrow & 336x+216x& = & 9-112 \\\Leftrightarrow & \color{red}{552} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{552} & & \\ & V = \left\{ \frac{-103}{552} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{5}{3})& = & 7x+\frac{9}{5} \\\Leftrightarrow & -16x+\frac{20}{3}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{+100} & = & \color{red}{105x} +27 \\\Leftrightarrow & -240x \color{red}{+100} \color{blue}{-100} \color{blue}{-105x} & = & \color{red}{105x} +27 \color{blue}{-105x} \color{blue}{-100} \\\Leftrightarrow & -240x-105x& = & 27-100 \\\Leftrightarrow & \color{red}{-345} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-345} & & \\\Leftrightarrow & x = \frac{73}{345} & & \\ & V = \left\{ \frac{73}{345} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{11})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 20x+\frac{25}{11}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x+ \frac{50}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{+50} & = & \color{red}{154x} +55 \\\Leftrightarrow & 440x \color{red}{+50} \color{blue}{-50} \color{blue}{-154x} & = & \color{red}{154x} +55 \color{blue}{-154x} \color{blue}{-50} \\\Leftrightarrow & 440x-154x& = & 55-50 \\\Leftrightarrow & \color{red}{286} x& = & 5 \\\Leftrightarrow & x = \frac{5}{286} & & \\ & V = \left\{ \frac{5}{286} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{9})& = & -7x+\frac{5}{9} \\\Leftrightarrow & -16x-\frac{20}{9}& = & -7x+\frac{5}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-144}{ \color{blue}{9} }x- \frac{20}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -144x \color{red}{-20} & = & \color{red}{-63x} +5 \\\Leftrightarrow & -144x \color{red}{-20} \color{blue}{+20} \color{blue}{+63x} & = & \color{red}{-63x} +5 \color{blue}{+63x} \color{blue}{+20} \\\Leftrightarrow & -144x+63x& = & 5+20 \\\Leftrightarrow & \color{red}{-81} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-81} & & \\\Leftrightarrow & x = \frac{-25}{81} & & \\ & V = \left\{ \frac{-25}{81} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & 6x+\frac{3}{11} \\\Leftrightarrow & 25x-\frac{15}{4}& = & 6x+\frac{3}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1100}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{264}{ \color{blue}{44} }x+ \frac{12}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1100x \color{red}{-165} & = & \color{red}{264x} +12 \\\Leftrightarrow & 1100x \color{red}{-165} \color{blue}{+165} \color{blue}{-264x} & = & \color{red}{264x} +12 \color{blue}{-264x} \color{blue}{+165} \\\Leftrightarrow & 1100x-264x& = & 12+165 \\\Leftrightarrow & \color{red}{836} x& = & 177 \\\Leftrightarrow & x = \frac{177}{836} & & \\ & V = \left\{ \frac{177}{836} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{3}{2})& = & -9x+\frac{2}{7} \\\Leftrightarrow & -35x-\frac{21}{2}& = & -9x+\frac{2}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-490}{ \color{blue}{14} }x- \frac{147}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{4}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -490x \color{red}{-147} & = & \color{red}{-126x} +4 \\\Leftrightarrow & -490x \color{red}{-147} \color{blue}{+147} \color{blue}{+126x} & = & \color{red}{-126x} +4 \color{blue}{+126x} \color{blue}{+147} \\\Leftrightarrow & -490x+126x& = & 4+147 \\\Leftrightarrow & \color{red}{-364} x& = & 151 \\\Leftrightarrow & x = \frac{151}{-364} & & \\\Leftrightarrow & x = \frac{-151}{364} & & \\ & V = \left\{ \frac{-151}{364} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{4}{3})& = & -9x+\frac{8}{5} \\\Leftrightarrow & 25x+\frac{20}{3}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{375}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 375x \color{red}{+100} & = & \color{red}{-135x} +24 \\\Leftrightarrow & 375x \color{red}{+100} \color{blue}{-100} \color{blue}{+135x} & = & \color{red}{-135x} +24 \color{blue}{+135x} \color{blue}{-100} \\\Leftrightarrow & 375x+135x& = & 24-100 \\\Leftrightarrow & \color{red}{510} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{510} & & \\\Leftrightarrow & x = \frac{-38}{255} & & \\ & V = \left\{ \frac{-38}{255} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{9})& = & 3x+\frac{3}{10} \\\Leftrightarrow & -8x+\frac{8}{9}& = & 3x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-720}{ \color{blue}{90} }x+ \frac{80}{ \color{blue}{90} })& = & (\frac{270}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -720x \color{red}{+80} & = & \color{red}{270x} +27 \\\Leftrightarrow & -720x \color{red}{+80} \color{blue}{-80} \color{blue}{-270x} & = & \color{red}{270x} +27 \color{blue}{-270x} \color{blue}{-80} \\\Leftrightarrow & -720x-270x& = & 27-80 \\\Leftrightarrow & \color{red}{-990} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-990} & & \\\Leftrightarrow & x = \frac{53}{990} & & \\ & V = \left\{ \frac{53}{990} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{7})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-50} & = & \color{red}{-245x} +56 \\\Leftrightarrow & -350x \color{red}{-50} \color{blue}{+50} \color{blue}{+245x} & = & \color{red}{-245x} +56 \color{blue}{+245x} \color{blue}{+50} \\\Leftrightarrow & -350x+245x& = & 56+50 \\\Leftrightarrow & \color{red}{-105} x& = & 106 \\\Leftrightarrow & x = \frac{106}{-105} & & \\\Leftrightarrow & x = \frac{-106}{105} & & \\ & V = \left\{ \frac{-106}{105} \right\} & \\\end{align}\)