Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{10})& = & -8x+\frac{6}{5} \\\Leftrightarrow & 15x+\frac{9}{10}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{+9} & = & \color{red}{-80x} +12 \\\Leftrightarrow & 150x \color{red}{+9} \color{blue}{-9} \color{blue}{+80x} & = & \color{red}{-80x} +12 \color{blue}{+80x} \color{blue}{-9} \\\Leftrightarrow & 150x+80x& = & 12-9 \\\Leftrightarrow & \color{red}{230} x& = & 3 \\\Leftrightarrow & x = \frac{3}{230} & & \\ & V = \left\{ \frac{3}{230} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{2}{5})& = & 5x+\frac{5}{4} \\\Leftrightarrow & -24x-\frac{12}{5}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-480}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -480x \color{red}{-48} & = & \color{red}{100x} +25 \\\Leftrightarrow & -480x \color{red}{-48} \color{blue}{+48} \color{blue}{-100x} & = & \color{red}{100x} +25 \color{blue}{-100x} \color{blue}{+48} \\\Leftrightarrow & -480x-100x& = & 25+48 \\\Leftrightarrow & \color{red}{-580} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-580} & & \\\Leftrightarrow & x = \frac{-73}{580} & & \\ & V = \left\{ \frac{-73}{580} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{7})& = & 7x+\frac{5}{7} \\\Leftrightarrow & -9x-\frac{15}{7}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-63}{ \color{blue}{7} }x- \frac{15}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -63x \color{red}{-15} & = & \color{red}{49x} +5 \\\Leftrightarrow & -63x \color{red}{-15} \color{blue}{+15} \color{blue}{-49x} & = & \color{red}{49x} +5 \color{blue}{-49x} \color{blue}{+15} \\\Leftrightarrow & -63x-49x& = & 5+15 \\\Leftrightarrow & \color{red}{-112} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-112} & & \\\Leftrightarrow & x = \frac{-5}{28} & & \\ & V = \left\{ \frac{-5}{28} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & -3x+\frac{3}{7} \\\Leftrightarrow & 8x+\frac{12}{5}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+84} & = & \color{red}{-105x} +15 \\\Leftrightarrow & 280x \color{red}{+84} \color{blue}{-84} \color{blue}{+105x} & = & \color{red}{-105x} +15 \color{blue}{+105x} \color{blue}{-84} \\\Leftrightarrow & 280x+105x& = & 15-84 \\\Leftrightarrow & \color{red}{385} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{385} & & \\ & V = \left\{ \frac{-69}{385} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{7})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -8x+\frac{10}{7}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+50} & = & \color{red}{-315x} +42 \\\Leftrightarrow & -280x \color{red}{+50} \color{blue}{-50} \color{blue}{+315x} & = & \color{red}{-315x} +42 \color{blue}{+315x} \color{blue}{-50} \\\Leftrightarrow & -280x+315x& = & 42-50 \\\Leftrightarrow & \color{red}{35} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{35} & & \\ & V = \left\{ \frac{-8}{35} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{3}{7})& = & -5x+\frac{5}{2} \\\Leftrightarrow & 8x+\frac{12}{7}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{112}{ \color{blue}{14} }x+ \frac{24}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 112x \color{red}{+24} & = & \color{red}{-70x} +35 \\\Leftrightarrow & 112x \color{red}{+24} \color{blue}{-24} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{-24} \\\Leftrightarrow & 112x+70x& = & 35-24 \\\Leftrightarrow & \color{red}{182} x& = & 11 \\\Leftrightarrow & x = \frac{11}{182} & & \\ & V = \left\{ \frac{11}{182} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{7})& = & -7x+\frac{5}{12} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-840}{ \color{blue}{84} }x- \frac{120}{ \color{blue}{84} })& = & (\frac{-588}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -840x \color{red}{-120} & = & \color{red}{-588x} +35 \\\Leftrightarrow & -840x \color{red}{-120} \color{blue}{+120} \color{blue}{+588x} & = & \color{red}{-588x} +35 \color{blue}{+588x} \color{blue}{+120} \\\Leftrightarrow & -840x+588x& = & 35+120 \\\Leftrightarrow & \color{red}{-252} x& = & 155 \\\Leftrightarrow & x = \frac{155}{-252} & & \\\Leftrightarrow & x = \frac{-155}{252} & & \\ & V = \left\{ \frac{-155}{252} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{3}{11})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 24x+\frac{18}{11}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1056}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1056x \color{red}{+72} & = & \color{red}{-220x} +99 \\\Leftrightarrow & 1056x \color{red}{+72} \color{blue}{-72} \color{blue}{+220x} & = & \color{red}{-220x} +99 \color{blue}{+220x} \color{blue}{-72} \\\Leftrightarrow & 1056x+220x& = & 99-72 \\\Leftrightarrow & \color{red}{1276} x& = & 27 \\\Leftrightarrow & x = \frac{27}{1276} & & \\ & V = \left\{ \frac{27}{1276} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{5})& = & -5x+\frac{7}{3} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{-75x} +35 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +35 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & -180x+75x& = & 35+36 \\\Leftrightarrow & \color{red}{-105} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-105} & & \\\Leftrightarrow & x = \frac{-71}{105} & & \\ & V = \left\{ \frac{-71}{105} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{4}{11})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -12x-\frac{24}{11}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{72}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-72} & = & \color{red}{-165x} +88 \\\Leftrightarrow & -396x \color{red}{-72} \color{blue}{+72} \color{blue}{+165x} & = & \color{red}{-165x} +88 \color{blue}{+165x} \color{blue}{+72} \\\Leftrightarrow & -396x+165x& = & 88+72 \\\Leftrightarrow & \color{red}{-231} x& = & 160 \\\Leftrightarrow & x = \frac{160}{-231} & & \\\Leftrightarrow & x = \frac{-160}{231} & & \\ & V = \left\{ \frac{-160}{231} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{5}{7})& = & -9x+\frac{7}{8} \\\Leftrightarrow & 4x-\frac{10}{7}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{224}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 224x \color{red}{-80} & = & \color{red}{-504x} +49 \\\Leftrightarrow & 224x \color{red}{-80} \color{blue}{+80} \color{blue}{+504x} & = & \color{red}{-504x} +49 \color{blue}{+504x} \color{blue}{+80} \\\Leftrightarrow & 224x+504x& = & 49+80 \\\Leftrightarrow & \color{red}{728} x& = & 129 \\\Leftrightarrow & x = \frac{129}{728} & & \\ & V = \left\{ \frac{129}{728} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{5}{4})& = & 8x+\frac{6}{11} \\\Leftrightarrow & 21x-\frac{35}{4}& = & 8x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{924}{ \color{blue}{44} }x- \frac{385}{ \color{blue}{44} })& = & (\frac{352}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 924x \color{red}{-385} & = & \color{red}{352x} +24 \\\Leftrightarrow & 924x \color{red}{-385} \color{blue}{+385} \color{blue}{-352x} & = & \color{red}{352x} +24 \color{blue}{-352x} \color{blue}{+385} \\\Leftrightarrow & 924x-352x& = & 24+385 \\\Leftrightarrow & \color{red}{572} x& = & 409 \\\Leftrightarrow & x = \frac{409}{572} & & \\ & V = \left\{ \frac{409}{572} \right\} & \\\end{align}\)